Human Universe (24 page)

General Relativity, like the Standard Model, contains a coupling constant encoding the measured strength of gravity:
G
, Newton’s gravitational constant. The amount of dark energy is inserted by hand, in accord with observations, as was the case for the strengths of the forces and the masses of the particles in the Standard Model.

General Relativity and the Standard Model are the rules of the game. They contain all our knowledge of the way that nature behaves at the most fundamental level. They also contain almost all the properties of our universe that we think of as fundamental. The speed of light, the strengths of the forces, the masses of the particles (encoded as the strength of their interaction with the Higgs Bosons via the Yukawa couplings) and the amount of dark energy are all in these equations. In principle, any known physical process can be described by them. This is the current state of the art, but it doesn’t mean that we know how everything works and can all retire, by a long shot or well-timed cover drive.

Most games are skin-deep, but cricket goes to the bone.

John Arlott and Fred Trueman

I timed a cover drive properly once when I was 14 years old playing at Hollinwood Cricket Club near Oldham. Front foot, head in line with the ball, sweet sound of the middle, four runs. I know what I have to do, but I never did it quite as well again. Cricket is an art built on simple rules, first codified by the members of the Marylebone Cricket Club on 30 May 1788; a significant date in world history according to historians with good taste. Those original laws still form the basis of the game today. There are 42 of them, and they define the framework within which each game evolves. Yet despite the rigid framework, no two games are ever alike. The temperature and humidity of the air, a light scatter of dew on the grass, the height of grass on the wicket, and hundreds of other factors will subtly shift and change throughout the game. More importantly, the players and umpires are each complex biological systems whose behaviour is far from predictable, with the exception of Geoffrey Boycott. The presence of so many variables makes the number of possible permutations effectively infinite, which is why cricket is the most interesting of human pursuits excluding science, sex and wine tasting.

Knowledge of the laws is therefore insufficient to characterise the infinite magic of the game. This is also true for the universe. The laws of nature define the framework within which things happen, but do not ensure that everything that can happen will happen in a finite universe – that rather obscure ‘finite’ caveat will be important for us later on. Virtually all of science beyond particle physics and theoretical cosmology is concerned with the complex outcomes allowed by the laws rather than the laws themselves, and in a certain sense our solipsistic initial question ‘Why are we here?’ is also a question about outcomes rather than laws. The answer to the question ‘Why did England beat Australia in the great Ashes series of 2005?’ is not to be found in the MCC rule book, and similarly the natural world that emerges from the Standard Model and General Relativity cannot be understood simply by discovering the laws themselves.

It’s worth noting that the laws of nature were not written by the MCC, or even the committee of Yorkshire County Cricket Club. We had to work them out by watching the game of the universe unfold, which makes their discovery even more wonderful. Imagine how many matches would have to be viewed in order to deduce the laws of cricket, including but not restricted to the Duckworth Lewis method? The great achievement of twenty-first-century science is that we’ve managed to work out the laws of nature by doing just this; observing many millions of complex outcomes and working out what the underlying laws are.

The Standard Model, then, cannot be used to describe complex emergent systems such as living things. No biologist would attempt to understand the way that ATP is produced inside cells using the Standard Model Lagrangian and no telecommunications engineer would use it to design an optical fibre. They wouldn’t want to even if they could; you wouldn’t gain any insight into how a car engine works by starting off with a description of its constituent subatomic particles and their interactions. So whilst it is important that we have a detailed model of nature at the level of the known fundamental building blocks, we must also understand how the complexity we observe around us emerges from these simple laws if we are to make progress with our difficult ‘Why?’ question.

On Monday 27 March 1905 at 8.30am, William Jones arrived at Chapman’s Oil and Colour Shop on Deptford High Street ready for a day’s work. Jones normally arrived a few minutes after the shop manager Thomas Farrow had raised the shutters. On this particular Monday, however, the shutters were down. Farrow lived with his wife Anne above the shop, but no matter how hard Jones knocked on their door, there was no response. This was a most unusual start to the day, and his concern increased when a glimpse through a window revealed chairs strewn across the floor of the normally tidy shop. Jones and another local resident forced the door, to be confronted by Farrow lying dead in a pool of blood. Anne had been similarly bludgeoned in her bed, although she clung to life for four more days without regaining consciousness.

Such scenes were not uncommon in Edwardian London. The reason that this crime is of note is because it was the first in the world to use a new technology to catch and convict the killers. On an inner surface of the empty cash box, the police noticed a fingerprint. They already had a suspect: a local man named Alfred Stratton, who was arrested three days later along with his brother Albert. The Strattons’ fingerprints were taken, and a positive match was made between the cash-box print and Alfred Stratton’s right thumb. Although fingerprints were never used before in a murder case, expert witnesses convinced the jury that the complex patterns of the cash-box fingerprint could only belong to Alfred Stratton. The jury took just two hours to find the Stratton brothers guilty of murder, and the pair were sentenced to death by hanging, with justice swiftly dispatched on 23 May.

Take a look at your fingerprints now; there is seemingly endless complexity in the swirls and ridges. Since every human being carries different fingerprints on the hands and the soles of their feet (which aren’t fingerprints, but there isn’t a word for them), the size of database required to characterise every human being’s fingerprints would be colossal. One of the most important properties of nature, however, is that the blueprints for the construction of the natural world are far simpler than the natural world itself. In modern language, there is a tremendous amount of data compression going on. The instructions to create fingerprints are far simpler than the fingerprints themselves, and more than that, the same instructions, run over and over again from slightly different starting points in the embryonic stage of our development, always lead to different fingerprints. This behaviour shouldn’t come as a surprise. The sweep of desert dunes or the patterns in summer clouds are all described by a handful of simple laws governing how sand grains or water droplets behave when agitated by shifting air currents, buffeted by chaotic thermals and winds and re-ordered by the action of the forces of nature. And yet from a simple recipe, complexity emerges.

The quest to understand how the boundless variety of the natural world emerges from underlying simplicity has been a central theme in philosophical and scientific thought. Plato attempted to cast the world available to our senses as the distorted and imperfect shadow of an underlying reality of perfect forms, accessible through reason alone. The modern expression of Plato’s ethereal dualism was captured eloquently by Galileo, 500 years ago: ‘The book of nature is written in the language of mathematics’. The challenge is not only to discern the underlying mathematical behaviour of the world, but also to work back upwards along the chain of complexity to explain how those forms that Plato would have defined as imperfect arise from the assumed lower-level perfection. A rather beautiful early example of this quest is provided by Galileo’s illustrious contemporary, Johannes Kepler.

Johannes Kepler is rightly best known for his laws of Planetary Motion that paved the way for Newton to write
Principia
. Hidden within his illustrious CV, however, is a publication that had a rather more whimsical earthbound ambition. Two years after publishing the first part of
Astronomia Nova
in 1609, Kepler published a short 24-page paper entitled
De nive sexangula
– On the Six-Cornered Snowflake
. It is a beautiful example of a curious scientific mind at work. In the dark December of 1610, Kepler was walking across the Charles Bridge in Prague when a snowflake fell on the lapel of his coat. In the freezing night he stopped and wondered why this ephemeral sliver of ice possessed a six-sided structure, in common with all other snowflakes, notwithstanding their seemingly infinite variation. Others had noticed this symmetry before, but Kepler realised that the symmetry of a snowflake must be a reflection of the deeper natural processes that underlie its formation.

‘Since it always happens when it begins to snow, that the first particles of snow adopt the shape of small six-cornered stars, there must be a particular cause,’ wrote Kepler, ‘for if it happened by chance, why would they always fall with six corners and not with five, or seven?’ Kepler hypothesised that this symmetry must be due to the nature of the fundamental building blocks of snowflakes. This stacking of frozen ‘globules’, as he referred to it, must be the most efficient way of building a snowflake from the ‘smallest natural unit of a liquid like water’.

To my mind, this is a leap of genius and a tremendously modern way of thinking about physics. The study of symmetry in nature lies at the very heart of the Standard Model, and abstract symmetries known as gauge symmetries are now known to be the origin of the forces of nature. This is why the force-carrying particles in the Standard Model are known as gauge bosons. Kepler was searching for the atomic structure of snow before we knew atoms existed, motivated by the observation of a symmetry in nature – the six-sided shape of all snowflakes. The inspiration for this idea, which is way ahead of its time, came from a peculiar source. In the years leading up to the publication of
De nive sexangula
, Kepler had been in communication with Thomas Harriot, an English mathematician and explorer. Amongst multiple claims to fame, Harriot was the navigator on one of Sir Walter Raleigh’s voyages to the New World, and had been asked to solve a seemingly simple mathematical problem. Raleigh wanted to know how best to stack cannonballs to make the most efficient use of the limited space on the ship’s deck. Harriot was driven to exploring the mathematical principles of sphere packing, which in turn led him to develop an embryonic model of atomic theory and inspire Kepler’s consideration of the structure of snowflakes. Kepler imagined replacing cannonballs with globules of ice, and supposed that the most efficient arrangement creating the greatest density of globules was the six-sided hexagonal form he observed in the snowflake on his shoulder. Kepler also observed hexagonal structures across the natural world, from beehives to pomegranates and snowflakes, and presumed that there must be some deeper reason for its ubiquity.