The curves of life (1914) by Theodore Andrea Cook, PDF ebook

The curves of life with numerous illustrations

The curves of life with numerous illustrations


being an account of spiral formations and their application to growth in nature, to science and to art; with special reference to the manuscripts of Leonardo da Vinci

When my attention was first turned to the subject of spiral formations, more than twenty years ago, it was in connection with an artistic problem, rather than with a biological question, that I investigated them. 

As was inevitable, I found myself obliged to examine the forms of natural life; and I learnt that this extraordinary and beautiful formation is to be seen throughout organic nature, from the microscopic foraminifera and from life forms even smaller still. In shells, in plants, in the bodily structures of men and animals, the spiral formation is certainly a common factor in a multitude of phenomena apparently widely different.

 As my investigations broadened I had to secure the assistance of expert authorities in separate divisions of research, to whom I cannot be sufficiently grateful, and I mention this in order to answer the obvious criticism that no one man would in these days be considered competent to deal with the separate branches of knowledge which my inquiry has gradually necessitated. This is one reason why anyone who is interested in the rough programme sketched in my first chapter may choose his own path to the last one, which sums up the whole. He may read of shells in Chapters III. and IV. and X.; of plants and flowers in Chapters V. to IX. and in XI.; of horns in Chapter XII.; of anatomy and lefthandedness in the two next; of the growth of patterns in the fifteenth; of architecture in XVI. and XVII.; of the attribution of a building to Leonardo da Vinci in XVIII.; or of Albert Diirer's mathematics in the nineteenth. 

The mere recitation of so varied a list of necessary subjects leads me here to lay immediate stress upon the value of human curiosity about the world around us, upon that thirst for a rational explanation of phenomena which Comte so loftily despised, which Aristotle and Spinoza so clearly acknowledged. Such writers as Mach and Kirchhoff seem to me to have gone back to Comte's most vulnerable position when they limit the use of science to the description. For we do not want mere catalogues. If every generation of great thinkers had not thirsted for explanations also, we should never have evolved the complexity and beauty of modern science at all. Only by some such discovery of relationships can we ever try to deal rationally with that " perpetual flux " which (as is more and more clearly recognised) the phenomena of life and nature present. 

There is a deep-seated instinct that attracts our minds towards those " desperate feats of thinking " which have achieved the greater victories of humanity; and it is by them that we must surely stand the ultimate test of our survival. Modern research is gradually becoming free both from accidental prejudices and from meretricious standards. There is a new spirit at work upon constructive philosophy which has never been so urgent, so creative, or so strong; and knowledge has become much more accessible at the very time when its transmission over the whole world has been enormously facilitated by new methods of communication.


 This means that thought is becoming clearer and more critical, and that breadth of outlook and freedom of imagination have resulted which must impel alike the laziest to look about him, and the busiest to linger and inquire. Some ripple of that widespread impulse has produced this book; but the very process just described has created its own difficulty; for specialisation is in these days so sternly necessitated by the obvious benefits of the division of labour, that it becomes an increasingly complicated task to put the various results of separate investigations in their true relationship with each other. Analysis, therefore, has been my first aim. 

Not till my last two chapters have I ventured to elaborate the synthesis which completes and justifies my catalogue of details, and for this, I have ventured to propose a convenient instrument that may be usefully employed in dealing with the varied multiplicity of natural phenomena. It may be said that with very few exceptions the spiral formation is intimately connected with the phenomena of life and growth. When it is found in inorganic phenomena the logarithmic spiral is again connected with those forms of energy which are most closely comparable with the energy we describe as life and growth, such, for instance, as the mathematical definition of electrical phenomena, or the spiral nebulse of the astronomer. Newton arrived at his theory of the movements of the celestial bodies in our own solar system by postulating perfect movement and by calculating from that the apparently erratic orbits of the planets. In just the same way may it not be possible to postulate perfect growth and from that to calculate and define the apparently erratic growths and forms of living things? 

Some contents of the book

Growth and Beauty and Spiral Formations — Letters from Sir E. Ray Lankester and Dr A. R. Wallace— Measurement of Bones — Nature not mathematically exact — Gravity and Perfect Motion: Spirals and Perfect Growth— Spirals in Shells, Whirlwinds, Human Organs, Nebula;, etc. — Classification, Utility, and Antiquity of Spirals— Need of Theory
pp. I — 22 
CHAPTER II
MATHEMATICAL DEFINITIONS
Spiral Appearances subjective — Flat Spirals — Left Hand and Right Hand — Conical and Cylindrical — Ionic Volute drew by means of a Shell — Ways of making Spirals — Curious Nomenclature used by Botanists . . . . pp. 2,^ — 40
CHAPTER III
UPRIGHT SPIRALS IN SHELLS
Formation of Spirals in Shells — Tube coiled round Axis — Life History of a Series in One Shell — Acceleration and Rotation — Natural Selection — Adjustment to Environment — Survival and Spiral Variation — Right-hand and Left-hand Shells — Ammonite and Nautilus — External and Internal Spirals — Supporting the Central Column — Comparison with Insects and Plants — Multiple Spirals . . . pp. 41 — 56

CHAPTER IV
FLAT SPIRALS IN SHELLS
Nautilus and Logarithmic Spiral — Equiangular Spiral a Manifestation of Energy — Deviation from Curve of Perfect Growth — Leonardo da Vinci as Student of Shells — Work of Professor Goodsir — Varying Inversely as the Cube and the Square — Significance of the Position of the Siphuncle — Vertical and Horizontal Views of Shells and Plants . . . pp. 57 — 80
CHAPTER V
BOTANY — THE MEANING OF SPIRAL LEAF ARRANGEMENTS
Provision for Air and Sunlight — Overlapping of Old Leaves by Young — Advantages of Overlapping in Intense Glare — Spiral Plan for Minimum Overlap — The Ideal Angle — Fibonacci Series — Mr. A. H. Church on Logarithmic Spirals in Phyllotaxis
 

 
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