Customer Reviews

A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science

5 star:		(56)
4 star:		(3)
3 star:		(3)
2 star:		(2)
1 star:		(6)

 

 

This is a very well written book that relates some basic concepts in geometry to science, architecture and life. Each of the ten chapters is about a geometric shape and Mr. Schneider shows how to construct it using only compass and straight-edge. The author begins every construction from a circle, and every line is shown as the intersection of two or more circles. This is consistent with his assertion in Chapter One that the circle is Unity, but I believe it is also more accurate geometrically.
Mr. Schneider gets into the Platonic Solids, explains the golden section and its use in architecture and nature, shows the regularity in nature and a lot more. This is a very educational book that covers a lot of ground, and does so in an entertaining way.
What I really like about the book is the author's ability to bring geometry to life. There are many diagrams, drawings and pictures which make it easy to follow the text.
The book is written for the layman, not the mathematician. If you are looking for a more rigorous introduction to geometry, try reading H.M.S. Coxeter (if you can!).
This book would be a nice companion to "The Power of Limits" by Doczi, 'The Geometry of Art and Life" by Ghyka, and "The Divine Proportion" by Huntley.
If I had to recommend only one book about geometry for the average reader, this book would be my first choice.

Who knew that our universe is such a spectacularly ordered place? Michael Schneider takes us on a fantastic voyage through the primary numbers one through ten, and shows us how numbers and geometry have helped shape our world and the cosmos. Why is a manhole cover round? Because a circle, whose diameter is everywhere equal, is the only shape that won't fall into its own hole. Three symbolizes harmony -- life has a beginning, a middle and an end. Life forms are often characterized by pentagons (cut an apple in half crosswise and look at the seeds), while six is the number of structure-function-order, as seen in the hexagonal symmetry of crystals and snowflakes. This book is by no means for math majors only; even math dummies like this reviewer will find themselves totally caught up. Art and design students especially will appreciate the almost infinite variety of possible designs suggested within each primary number and the basic shapes (circle, square and triangle). Schneider also shows how, with a compass, pencil and straightedge, one can construct one's own symbolic universe. I came away from this book not only enlightened on the subject of symbolic math, but blown away by the relationship between geometry and religion. Because reading this book makes one realize that the universe is not random, as we see it within our limited scope, but has a definite function and order, and perhaps only the God who created it according to His plan can see it whole.

I'm quite biased because I'm the author. Just thought I'd mention that it took over 20 years of research and 2 years to write & illustrate (500 illus!), plus hundreds of relevant quotations in the side margins. The numbers 1-10 (&12) are the key to the code of nature's designs, and are the basis of an ancient symbolic language used to design the arts, crafts & architecture worldwide. Each of 10 chapters looks at that number & its related shapes, as they appear in nature's beautiful forms, in art, in symbolism, and as archetypes of our own spiritual nature. Shapes are the characters of the alphabet in which the Book of Nature is written, and this is a "math" book with no math (the kind of cold "math" we were shown in school, anyway). Some people call it "sacred geometry". This book will save you years of research, and show you how to appreciate the shapes of nature as a symbolic language familiar to our deepest self. Every shape has a "meaning" and this book shows you what they are. Reviews (Parabola Journal Winter 95, New Age Journal 8/95, etc, all remark how "accessible" it is. I hope you enjoy it. If you read it, write me, if you like. Happy Trails! Michael S. Schneider NYC

I really did not like math when I was in school. What was the point? Manipulating a bunch of abstract concepts for the mere sake of doing the work. Why don't they teach this type of math in schools? Well anyway, I believe that you can not truly understand life, religion and the world around us without taking a long look at this beautiful knowledge that has been preserved for so many millenia. If you want to look into the mind of God, study the rules by which he organized the universe. And if you think that everything around you is chaos, read this book and look again. You will find that everything from the microscopic to universal aggregate is striving toward simple and beautiful geometric patterns. The author does a nice job of giving to the reader a piece of his deep understanding and love for this subject. This book is more of a textbook and is neatly organized. I highly recommend also getting a copy of Sacred Geometry: Philosophy and Practice by Robert Lawlor. It has lots of excercises to emerse the student in the beauty of geometric relationships. These two books go hand-in-hand. Lastly, I can not emphasize enough how much more understanding I gained about religion by learning geometry. Does that sound bizzare? I suppose, but it is true.

What I find fascinating about this book is the way it explores relationships between numbers, and why geometry is not as artificial and arbitrary as most people think today. For example, the REASON why bees construct honeycombs from hexagonal cells.

The author knows his Pythagoras, but unfortunately he plays fast and loose with a few other things. One example is the "red devil" image of Set that doesn't exist anywhere in ancient Egyptian literature or art. And throughout the book he seems to go a little too far into New Age mystical fuzziness for my tastes.

Overall I'd recommend the book, but any statements that aren't purely mathematical, take with a grain of salt. The math itself is fascinating enough without the embellishments.

This book is a labor of love...and discipline, and hard work. The quotations given on the wide margins of most pages are worth the price of admission alone. For instance, "The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal (William James). It is also the theme of the book.

But that is only the beginning. There are at least two, to as many as ten, illustrations on each page, half being scientific, the other half artistic. My favorite combination is the splash crater of a milk drop on p. 11 and the Hindu deity Shiva Nataraj on p. 4. They form a complimentary pair visually and philosophically, both illustrating the monad, a generating center with a resultant circle of generated objects.

In the next two chapters, two intersecting circles lead to the tension-filled dyad whose resolution is in the triad, which breaks the tension by allowing expansion to another dimension.

In my words, this sounds a bit mystical and foggy, but Schneider provides just the right amount of background which carries you into the heart of the world of numbers, showing how they reflect both the scientific construction of the universe as well as artistic human creations.

The longest chapter is on the number five, which remarkably leads to the spiral, and to the generation of life. These are very valuable insights, much to be pondered. This chapter also contains an excellent discussion of the Golden Mean, the number 1.618..., which is often found in nature as well as in human expeience.

Just pick the book up sometime and glance at the quotations and illustrations. If you can resist buying it, you are a better man than I am.

The relationship between mathematics and the natural world has been argued about for 100's of years and the philosophy of mathematics has great significance when one looks back through the development of civilization and social structure. If you are interested in looking past the quantitative nature of numbers and discovering the entangled web of basic mathematics and human development then I could not recommend a better book.

This book is aimed at the generally inquisitive reader not the mathematics expert, there is little mathematics as we might recall from school. Instead Schneider draws on his considerable knowledge of history to give a whole new ( in fact ancient ) relevance to the numbers 1 to 10. There is nothing difficult in this book, it is written with the objective of enthusing the reader to look further rather than to teach.

I have a degree in mathematics and struggled with some of the more esoteric spiritual areas of the book but in general I enjoyed the read. The flow of the text was easy to read and logical and text is backed up by a considerable number diagrams and pictures although the quality of some of the images is lost in the news print quality paper.

It was very difficult to put this book down. Not only does Schneider evince a love and profound knowledge of his material, but he communicates his passion to the reader with a clarity uncharacteristic of many math exposeurs. It is a perfect teaching vehicle for parents and their children to foster a heartfelt respect for the mathematical majesty of nature, using examples from cultural history across the globe. His discussion of music and symbolic geometry is especially enlightening. This book should be required reading for any and all educators. A wonderful read!

I can't say enough about this fascinating book by this genius of an author. It is absolutely incredible, and the guy who wrote it is up there with Stephen Hawking as far as I'm concerned. To be able to make such astute observations about the mathematical and geometric patterns in the reality we live in and be able to document them in such a concise manner, all the while still managing to make the book a thoroughly enjoyable read is nothing short of ingenious. I'd give this book ten stars if I could. Twenty stars. It is fascinating to read, even if all you do is look at the pictures, and the second you get it in your hands I really think you'll agree.....but you ain't getting your hands on my copy :-)

I always enjoyed geometry in school, and this book opened up a whole new depth to the subject for me.

Reading the book, I dug out my compass, pencil, straight edge and 30, 60, and 90 degree angles to perform the various exercises recommended by the author.

Constructing the various geometrical figures I found to be akin to creating mandalas. You create something originating in the abstract that becomes concrete, that in turn ultimately becomes personally meaningful.

Also, I learned to view several churches in town on a completely different level.

Reading this book, you will never look at the numbers one through ten in quite the same way again.

The numbers take on significance and hint at something sublime and even transcendent.

Through this book, I discovered the rich undercurrents of pythagorean number theory, and their application to the rich christian architecture of the medieval churches.

With all the fuss over feng shui, this book draws from our decidedly western tradition, revealing we have our own undiscovered architectural history that has yet to capture the popular imagination.

A wonderful introduction, chapter by chapter, number by number, to sacred geometry and the pythagoreanism that runs through it.