n(t)=k/[1+(k/noâe"1)e-rt]

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 The Equations: Icons of Knowledge
How things are

THE SCOTTISH POET Don Paterson has said that the evolution of our species into conscious, upright beings âeoehas bequeathed us an increasingly terrible prospect: that of ourselves simultaneously within nature and outside it.âe Recognizing the profound comfort to be found in the description and representation of things, whether those things be horrific or beautiful, eternal or simply quotidian, Paterson also suggests a solution: âeoeArt serves to unite us with what is not us. [âe¦]It allows us to know ourselves as an expression of the universe, a word of its living speech, not as a book it once wrote and discarded.âe

The theoretical physicist Sander Bias would argue math equations provide a similar service. In The Equations: Icons of Knowledge, he presents seventeen of his favourite mathematical descriptions of nature, statements which nail down the interdependencies of earthly and cosmological elementsâe"motion, energy, gravity, mass, the determined march forward of seconds and minutes, hours and light years.



Sander Bias

Mortal and earthbound, an artistâe(TM)s choice of muses is limitedâe"to the landscapes, animals, and plants that surround us; to the heavens and gods above; to the mysteries inside usâe"happiness, faith, sanity, despair. So too are equations limited by certain immutable numbers; among them: Newtonâe(TM)s gravitational constant, which dictates the gravitational force of attraction between two bodies, be they childrenâe(TM)s toys lying on a bedroom carpet, or the planet Earth and a comet burning through empty space; the velocity of light, which Bias calls âeoenatureâe(TM)s speed limit,âe because anything traveling faster would have to be infinitely, impossibly heavy; and the cosmological constant, the (controversial, very-often disputed) rate at which the universe is expanding.

âeoeIf we were to take the same equations but change the values of these constants of nature,âe writes Bias, âeoethen nature would certainly be very different.âe If the constants held different valuesâe"if say pi, the mysterious number that lurks inherently in any perfect circle, were 5 instead of 3.14159265âe¦ and so onâe"the universe might exist in a totally different formâe"and we might not exist at all.

The Equations is in part an argument against what Bias calls âeoethe fashionable dogmaâe of avoiding equations in popular science writing. The book aims to refute the belief that the intricate nomenclature of a mathematical statement can only frustrate and discourage a lay reader. Bias wants us to focus on the sloping calligraphy, the fine balance, of each of his chosen equations; he wants us to appreciate the profound elegance and relative simplicity with which each approximates complex and dynamic natural processes. He wants us to see math for what it is, a language, just like any other, which for centuries and centuries has struggled, morphed and strained to communicate understanding, give brief moments of clarity during which one might get a fleeting glimpse of a tiny corner of the shape of existence.

Such a feat is as rarely achieved with mathematics as it is with prose, paint brush or cello, but Bias has collected equations that come close. Take the logistic equationâe"n(t) = k/[1 + (k/no âe" 1) e-rt] âe"in which n is the number of individuals in a population; no is the number of individuals alive at the beginning of any given time period in which a scientist is interested; r is the growth rate (the difference between death and birth rates), k is the maximum number of individuals a given ecosystem with limited quantities of nutrition can support, and n(t) is the number of individuals alive at any time t. This equation quantifies the growth and decay of populations such as bacteria in an unlucky host, lilies growing on a still pond, or a nomad tribe whose homeland desert only contains so many oases, only so much food.

Or take hydrodynamic equations, which are used to model gushing rivers, the destructive power of hurricanes, or the apocalypse of tsunamis. Thereâe(TM)s a chapter on the laws of thermodynamics, which document the battle between the universeâe(TM)s tendency toward maximum disorder and lifeâe(TM)s tendency toward the opposite: an order so rigid as to allow strands of DNA to build humming birdsâe(TM) wings, human brains, or tigersâe(TM) striped coats. And, of course, Bias wouldnâe(TM)t want you to overlook Einsteinâe(TM)s relativity equations, whose implications include gravityâe(TM)s ability to warp and bend space and time.

The book, Bias tells us, âeoeis a kind of landscape, with the equations as mountains,âe and that though some of the mountains are hard to climb, âeoeonce at the top the view is magnificent.âe The Equations is best enjoyed in this spirit, as its author sometimes bogs the text down with technical language. By skipping from one equation to the next, jumping from peak to peak, lingering just long enough to get a glimpse of the chaotic reality each manages to reign in, the reader can avoid the arduous climbing, littered, as it is, with clotted prose and physics jargon, and gaze from the heights, to feel like a small part of, and to be drawn closer to, a world, a universe, that ultimately can never fully be known.âe"Yohannes Edemariam

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