Forces of Nature. Andrew Cohen

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      Some of the many properties that have resulted in partial loss of the symmetry in the Solar System disc.

      There is a very important idea hiding here. We used the term ‘symmetry breaking’ to describe how the presence of a spin axis marks out a particular direction, resulting in an object deviating from the ‘perfect’ spherical shape that reflects the symmetry of the underlying law of Nature – in this case gravity. The disc of our Solar System is less symmetric than a sphere because it only remains the same when rotated about a particular axis in space – the spin axis. The symmetry has been partially lost. We might say that the symmetry of the law of gravity that created our Solar System has been hidden by the presence of a special direction in space – the spin axis. The spin itself came from the precise details of the collapse of the initial dust cloud almost 5 billion years ago, and the distribution of the spin between the Sun and planets depended on the precise speed of collapse, the density of the protoplanetary disc and myriad other subtle details over the history of the Solar System’s formation. This highlights one of the central challenges in modern science: which properties of the structures we see in Nature are reflections of the underlying laws of Nature, and which properties are determined by the history of formation or other influences? This is particularly difficult to answer when the physical systems in question are complicated. The shapes of planets, solar systems and galaxies, whilst astronomical in size, are easier to explain than the shapes of more mundane objects that we encounter every day. Let’s jump from simple planets to the most complex of all physical structures – living things. By exploring the symmetries and structures of living organisms, we can further explore the idea that the shape and form of physical objects are the result of a complex interplay between deep physical principles and the history of their formation.

Why does life come in so many shapes and sizes?

      The competition between the force of gravity and the electromagnetic force is responsible for smoothing the surface of planets and moons into spheres and limiting the maximum size of mountains on their surfaces. One of the central ideas in this book, which we will expand on in Chapter Three, is that there is no fundamental difference between inanimate things, such as planets, and living things, such as bacteria or human beings; all objects in the Universe are made of the same ingredients and are shaped by the same forces of Nature. We should therefore expect to see limits on the form and function of living things imposed by the laws of Nature. Basic physics is not the only driver of the structure of organisms, of course; there is also the undirected hand of evolution by natural selection, which moulds living things over time in response to their changing environment, their interaction with other living things, and the myriad available environmental niches. This creative interplay between the relentless determinism of physical laws and the seething, infinitely intertwined, ever-shifting genetic database of life on Earth is beautifully captured in Darwin’s closing lines of On the Origin of Species;

      ‘There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.’

      Another of our recurring themes is a celebration of the energetic curiosity of the early scientists. There is a breathless lyricism in their descriptions of ideas that remains relevant and essential; yet their presentation seems somehow unencumbered by the more serious and confining demands of modern professional science. There are great writers from the modern era who capture the logic, clarity and wonder of science – Richard Feynman, Richard Dawkins and Carl Sagan spring immediately to mind – but there is something exhilarating in seeing science evolving in words. The limits of the Renaissance authors are so often coterminous with the limits of all human knowledge that the investigations on the page are near real-time explorations rather than reminiscences from a well-trodden intellectual road. Perhaps this is what gives the old masters’ writings such exhilarating intellectual pace.

      Just as the force of gravity limits the maximum size of Earth’s mountains, so it limits the range of forms that natural selection can create, restricting the overall size of organisms that live on its surface. Four hundred years ago, Galileo Galilei explored the factors that define how big an animal can be; in common with Kepler and his snowflakes, he was operating at the edge of knowledge and ahead of his time. Discourses and Mathematical Demonstrations Relating to Two Sciences was Galileo’s final book, written whilst under house arrest and published in 1638 by the Dutch publisher Lodewijk Elzevir, because no country in the grip of the Inquisition would touch it. Any scientist reading this book will recognise the name: the Elsevier company, which took the publisher’s name, is today a leading scientific publisher. Galileo’s book is written in the style of a conversation between three men, Simplicio, Sagredo and Salviati, who each represent the author at a different age, and with a different level of knowledge. The characters wander from question to question during a conversation lasting four days, discussing and debating each subject before moving on to the next. The book has something of the voyeuristic pleasure of overhearing a conversation on a park bench – albeit in a park frequented by unusually thoughtful individuals. Galileo covers large swathes of the physics of the day, including a critical look at Aristotelian physics, accelerated motion, the motion of projectiles and the nature of infinity. His investigations also turned to the strength of materials and the limits placed on the size and form of structures, both animate and inanimate, by the laws of Nature.

      From what has already been demonstrated, you can plainly see the impossibility of increasing the size of structures to vast dimensions, either in art or in Nature. Likewise the impossibility of building ships, palaces or temples of enormous size in such a way that their oars, yards, beams, iron-bolts and, in short, all their other parts will hold together. Nor can Nature produce trees of extraordinary size, because the branches would break under their own weight; so also it would be impossible to build up the bony structures of men, horses or other animals so as to hold together and perform their normal functions if these animals were to be increased enormously in height. For this increase in height can be accomplished only by employing a material which is harder and stronger than usual, or by enlarging the size of the bones, thus changing their shape until their form and appearance suggest a monstrosity.

      Galileo states, for the first time, the relationship between volume and area, known today as the square–cube law; as an object grows in size, the volume grows faster than the surface area. Consider the example of a cube of sides measuring 2cm. The surface area is 6 x 2 x 2 = 24cm². The volume is 2 x 2 x 2 = 8cm³. If we double the length of the sides, the surface area is 96cm² and the volume is 64cm³. Double the length of the sides again and the surface area increases to 384cm² whilst the volume is 512cm³. And so on.

      This means that, as animals get larger, their volume, and therefore their mass, increases more rapidly than their surface area and the cross-sectional area of their bones. The consequence of this is that animals can’t simply be ‘scaled up’ in size. A mouse can’t be expanded to the size of an elephant because its skeleton would give way; that’s why an elephant has thicker legs relative to the rest of its body than a mouse. This ultimately places a fundamental limit on the maximum size of living things on land; the structural strength of bone, or wood in the case of trees, limits the mass of the organism in the same way that the structural strength of the rocks of the Earth’s crust limits the size of a mountain. On Mars, elephants could have thinner legs.

      Galileo realised there was an exception to this rule. Whereas gravity imposes a limit to the size and shape of animals on land, the constraints placed on living things СКАЧАТЬ