There are few books that juxtapose mathematics and aesthetics such as H. E Huntley’s, The Divine Proportion, A Study in Mathematical Beauty. The work offers an absorbing introduction to the features of mathematics which can be found in the innate structures of biological beings, chemical compounds and even artistic expressions. The book offers insights into how one can begin to view the relationships of mathematics to the actual world that is living and throbbing around us. Everything from biological growth to the sound of music is discusses in relationships to their mathematical structures.
Some of the these structures include the Golden ration, conic sections, spirals, Pythagorean numerology, Pascal’s triangle, the Fibonacci sequence and many other theorems. One of most intriguing sections of the book is the discussion on the mysterious Golden Mean. The author states that while the Golden Mean has always existed in math and in the physical universe, no one is quiet sure as to its origination and application. The concept of pi was used in the building of the Great Pyramids of Egypt, and the Greeks used it in the design proportions of the Parthenon.The author also discusses the famous Fibonacci Series, discovered in 1200 AD by Leonardo Fibonacci.
(pp. 157-158). First called the "Divine Proportion" in the 1500's, Huntley outlines the use of this Golden Mean in the paintings and sculptures on balance the search for the perfection of beauty. Leonardo Da Vinci used the ratio to construct the painting “The Last Supper,” using the dimensions for the fundamental placement of Christ and his disciples within the work.Astronomers also used the “Divine Proportion” to explain the orbit and elliptical nature of the movement of the planets around the sun.
In this sense, the author’s description of this proportion is used to evoke a sense of the divinity of nature in the reader. It is also an explanation used to allow the reader to understand how mathematics works to explain some of the deeper understandings of beauty and patterned repetition in the natural world. In this sense, a spiritual sense of connection emerges as one of the themes of this work.In this case of Pi (Phi), the actual numerical representation of the golden ration, we are witness to how one single number can play such a huge role in the natural world, as well as in the way human beings have been altering their physical universe for centuries. The intention of the work, an urge to embrace the connection between beauty and mathematics, is made clear through the following statement: “The theme of this book is the aesthetic appreciation of mathematics.Poincare's remark that ‘.
but for harmony beautiful to contemplate, science would not be worth following’ is applicable also to his own discipline, mathematics. K. Weierstrass's dictum that ‘No mathematician can be a complete mathematician unless he is also something of a poet,’ recalls Poincard's: ‘The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful. ’” (p. 1) Chapter three of the book, Analysis of Beauty, delves into a persuasive argument on the concept of beauty.The author maintains that beauty is not only a sensation of judgment within the human being.
It is a function of consciousness which has a precise mathematical representation based on proportions that are a function of the universe we live in. In this sense, whether we are a painter, a sculptor, an architect, a musician or a scientist, there seems to be a natural aesthetic, or harmony, which we can tap into in order to create a balanced product. According to Huntley, music represents another powerful area where mathematics emerges.The author argues that music is actually the “language of the mind par excellence. The author further develops his argument, stating that: “It is music that provides the strongest support for our thesis that aesthetic experience consists in the interaction between the universal primordial images buried in the unconscious and an external artifact or natural object which we call beautiful. ” The theory brilliantly develops itself, stating that music is not only stepped in the age old patterns and hard-wired structures of the entire universe, but that it is also possible to relate these familiar patterns in music to “archaic experiences of humanity.
Here we witness the fashion in which Huntley transposes mathematics into the human psychological realm and the deeper dominions of the human experience, whereby, “These universal emotionally charged experiences become effective when they are raised from the deep unconscious to the surface mind, and it happens that music, unlike any of the other arts, provides precise and powerful means of effecting this transfer. ” (pp. 18-22) Within this establishment of beauty as a natural phenomenon, the author then encourages us to consider whether this beauty in fact serves a purpose.Huntley’s analysis into the “Aesthetic Pleasure Universal” composes a statement on the purpose of enjoyment as a function of nature. He argues that “The power to appreciate beauty appears to be a human endowment and this suggests that we should seek its origin and its purpose in human nature-in that nature which distinguishes us from the animal creation.
” The reader is urged to connect with his or her higher purpose in life through the realization that he or she is essentially a creator, and that all joy derived from human existence is a result of the process of creating.This is the principle whether one is a poet, a scientist, a gardener or a carpenter. The only downside to the author’s analysis is the lack of the placement of man as not only a creative, but a destructive force as well. Within all humans and nature lies the innate movement towards creation, functioning parallel beside a destructive force.
Therein lies the ability to change, to manifest, to evolve, to live and to die. In this sense, the only critique of this beautifully poetic book is the lacking of the human and natural “dark side. ” Can we find Pi in our destructivity as well?In conclusion, the work of H. E. Huntley’s, The Divine Proportion, A Study in Mathematical Beauty, is a stunning piece that weaves mathematics into not only our daily life, but into the very fabric of what is means to have the experience of being human.
As the author sates, whether the interest of the reader “is focused on the golden cuboid, or the dodecahedron, or the logarithmic spiral or the genealogy of the drone bee, [one] should realize that, in the act of appreciation, he is re-enacting the creative act and, attracted by beauty, is experiencing himself the joy of creative activity.He is in fact, in Kepler's phrase, ‘thinking God's thoughts after Him. ’” And so, whether we are searching for aesthetic patterns for art and architecture, searching for the order of mathematics within a sunflower, or looking for insight into the human condition, this book offers a treasure trove of its own clues that will guide us towards realization.
