Book of the Month April 2005

A Beginner's Guide to Constructing the Universe, by Michael S. Schneider

This month's book of the month is "A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science, A Voyage from 1 to 10" by Michael S. Schneider. Schneider is an educator, and gives lectures about how math is used in science, art, and nature, which is the basis for this book. The reason I chose this particular book for the book of the month is because it has an interesting story to tell about a topic that not many people choose to take part of. While this book isn't math intensive, it is, essentially, a sort of math history book and may only appeal to people that have an interest in math. Interest in math isn't needed to enjoy it, however. The format of the book is simple: Schneider starts with the number one and works his way successively to the number ten, giving each number a bit of information.

Chapter One: Monad Wholly One

The names derived for each chapter come from the Greek word for the respective number it talks about; "one" is referred to as the "Monad." This chapter helps to set the stage for how the rest of the book is laid out for the reader. Schneider throws a lot of information in about the number one, and he talks about how it has been portrayed within various cultures. Although he gets into some of the spiritual aspect of the numbers as well, it doesn't necessarily detract from the other meanings that each number has. With each number he associates various things, especially shapes, that refer to each respective number. For the number one, he uses the circle, and points out some unique aspects for the circle and how it is used by humans, such as:

Manhole covers are round because the circle is the only shape that won't fall in on itself.
Plates and pizzas are round because they cover the most area and allow for more things to be on them.
Some tables are round (such as the legendary Round Table) to give the maximum surface area and to give those seated around it an equal standing.

He reinforces the idea of the importance of the number one and the shape of the circle by providing numerous examples of where they can be seen in nature. One last thing I like about this book is that there are very topical quotes throughout the chapters in the sidebars, and they provide a nice backdrop for what Schneider is trying to present.

Chapter Two: Dyad It Takes Two to Tango

If one is unique, two must be doubly so. In this chapter, Schneider talks about the number two. Two is a very important number for humans around the world, because it represents both opposites and dualities. Many religions and religious views include some aspect of two (Heaven/Hell, yin/yang, etc.), and our language is full of things that have polar opposites (North/South, up/down, etc.). Many things exist in pairs: male and female, protons and electrons. The concept of the Dyad is what is used to talk about them, as Schneider talks about in this chapter. For this chapter, the Dyad is represented by two intersecting circles, called the vesica piscis or mandorla. You might recognize this symbol by looking to the logo for Master Card, which is one red circle intersected by a yellow one.

Chapter Three: Triad Three-Part Harmony

One and two make three, the combination of the unique number and its dichotomous follower. Three represents the "child" of the numbers one and two. Three is achieved when you add together the total amount of numbers below it in succession, and can represent the basics to the beginning of counting. We have a natural tendency to lump things as threes (ready, set, go, for example). Three also represents a way to get away from a single entity, or the extrema of the spectrum. Schneider discusses just how important the number three is to humans, in the form of construction, but also how three shows up in nature.

Chapter Four: Tetrad Mother Substance

The number three can give is the recognizable shape of the triangle; the number four can add one more point to this triangle and make it three-dimensional. Schneider discusses the number four in terms of the geometric concept of volume. The triangular shape that is created by a fourth point is the tetrahedron, which is a very special shape in geometry. As Schneider points out, the tetrahedron is the only shape besides the sphere in which the points are equidistant from the center of the object. Another familiar shape created by four is the square. This is a pervasive structure found throughout cultures around the world. Schneider spends considerable time discussing the various attributes of the number four in this chapter.

Chapter Five: Pentad Regeneration

For the representative shape of the number five, Schneider uses the five-pointed star. This familiar symbol can be found on flags, restaurant reviews, and such. It can be used as a means of rating something of superior or excellent quality (think of choosing between a five-star hotel and a two-star hotel, for instance). Five is something that is also readily found in nature, from the number of fingers on your hand, to the shape of leaves. Another topic that Schneider introduces in this chapter is the concept of the Golden Rule, or the Golden Mean, a numerical representation that has both natural, and for some spiritual significance. Tied in closely with the Golden Mean is something referred to as the Fibonacci Sequence, which is a series of numbers where a successive number is derived from the sum of its two previous antecessors. The chapters are now getting to become more and more complex, as the numbers they describe do. This is a lengthy chapter, as Schneider has a lot to say about the Golden Mean, the Fibonacci's Sequence, and the significance of the number five.

Chapter Six: Hexad Structure-Function-Order

Now, more than halfway through the first ten numbers, comes the number six, this time represented by the hexagon. Again, more discussion about structures of six found artificially, and in nature. Schneider spends more time discussing the various aspects of the hexagon (and other six-sided shapes) found in many cultures throughout the world. There is a repeating pattern of how he addresses each number, and by now, this should be pretty obvious.

Chapter Seven: Heptad Enchanting Virgin

The shape for seven is the heptagon, a seven-sided shape that as the name of this chapter implies, represents a virginal state. Schneider tells us that ancient philosophers only considered seven number, (3,4,5,6,7,8,and 9); One and two were ignored, and anything higher than ten was a result of the seven numbers. Among the topics discussed in this chapter is music and light (ROYGBIV).

Chapter Eight: Octad Periodic Renewal

As in the previous chapters, Schneider defines a shape used by the number, this time it is the octagon for eight. In keeping with the previous chapters, he also points out some interesting cultural and spiritual significance's for the number eight, as well. Included in this chapter are discussions about music (octaves), DNA, and chess (a chessboard is composed of 64 squares, on an 8X8 grid). Specifically, the chessboard is seen to represent both the Earth and the phases of the Moon, discussed and illustrated quite well in this chapter.

Chapter Nine: Ennead The Horizon

Nine is represented by the shape of the nonagon. Schneider discusses some of the historical quotes and meanings attributed to the number nine; for example, the role of the number nine in the Dogon society in Mali, Africa. Tribes are divided into eights, and the number associated with the tribe plays in a role for marriage. This numbered association makes it so that someone from one tribe can marry someone from a tribe in which the tribal numbers add up to nine. For example, a woman from tribe numbered one will marry someone from tribe number eight. These added tribal numbers of nine are a representation of the Dogon chief, whose number is nine. Along with some interesting historical tidbits, he uses his role as a mathematician to detail some nifty tricks you can do with the number nine.

Chapter Ten: Decad Beyond Number

In this last chapter, dealing with the number ten, the chosen shape is the decagon, but talk about how to make other shapes with ten points or something similar out of the previous numbers is mentioned first. Ten is a very special number, since that is the counting number, the number of fingers and toes the average person has. Our entire system of counting is generally based on the number ten, called base ten. Logarithms, groups, powers of ten, etc., all rely on the number ten to work. Also included in this chapter is discussion about architecture.

Epilogue

Schneider takes a few brief pages at the end of the book to sort of pull together the significance of the last ten chapters. He suggests that now, since he has guided one through the basics of creating the universe, and has laid out the inner workings of things like geometry and architecture, that the reader should now be able to construct the universe.

Summary

This book is not the normal fair that I tend to read. While it does have some bearing on math, science, and nature, it seems more constructed for someone looking for spiritual meaning and philosophical ideas than anything with science. While Schneider does hand out some interesting information, that's about all he has to offer. I didn't find myself all that interested in the spiritual/philosophical stuff he added, but it might appeal to some. Considering that there aren't very many books regarding math or numbers out there that don't require one to do homework, however, this book provides a short break from the mundane world of arithmetic, if only for a short while. On a scale of monad to decad, I'd give it a hexad.

..::home::..

..::about::..

..::define::..

..::botm::..

..::faq::..

Navigation

Search

Calendar

Clock