Moonday Book Review: Sacred Geometry, the Negatives
Monday, September 3rd, 2007
Sacred Geometry
Deciphering the Code
Pursuant to my interest in the beauty of mathematical ideas, I decided to pick up a copy of Stephen Skinner’s book, Sacred Geometry, which surveys the beauty and synchronicities of whole numbers and geometric concepts. This is a beautify, however somewhat flawed book, and I’ve decided to break my review of it up into two posts highlighting its negative and positive aspects. I like to get the negatives out of the way up front, and leave off with positives. So…
Two Glaring Goof Ups
Da Vinci’s Drawings
of the Platonic Solids
(Tetrahedron, Hexahedron,
Octahedron, Icosahedron,
Dodecahedron)
In the section on the five platonic solids, Skinner notes that the hexahedron (earth) and octahedron (air) are a pair, meaning it’s possible to create one from the other by connecting the vertices to the centers of the faces. Correct, but then he writes that the icosahedron (water) and tetrahedron (fire) are also a pair in this sense, and the dodecahedron (ether) is a pair unto itself; therefore, poetically, ether comes from ether.
Wrong. It’s the icosahedron and dodecahedron that are a pair, each forming the other. I know this because, for a brief phase in my life, I was spending my leisure time getting schnookered and playing with Zome Tools, and have built this association myself. It is the tetrahedron that makes itself; therefore, not quite so poetically, fire comes from fire.
Skinner, like most skips–or doesn’t know about–what I think is the most fascinating aspect of the icosohedron platonic solid: the fact that it is possible to generate three golden rectangles inside it by connecting the vertices. I am so enchanted by this fact, that I keep a ZomeTool model of an icosahedron with the interlaced golden rectangles on my desk at work. It serves as a warning to my geeky coworkers that this desk is my territory:
Ryan’s Icosahedron With
Golden Rectangles Highlighted
Now, as Professor Bender will instruct, ignore the cross lines in the figure, but note the rectangle, which has proportions according to the golden rectangle. Now imagine Dr. Bender rotating the object 180-degrees along the horizontal axis, and the horizontal line will reveal another golden rectangle. A 180-degree twist on the vertical axis, and the vertical line will reveal a golden rectangle. Doesn’t that just make your eyes glaze over with indifference???
Me too. Here’s some good pictures of what I’m talking about. Let’s move on.
When discussing prime numbers, Skinner cites Peter Plichta’s Prime Number Circle, which is titled “Prime Number Cross” in the reference I found, but this is an obscure mathematical construction. I suspect his reasoning for using it is Plichta’s focus on figuring out “God’s Secret Formula” from primes, which he didn’t… or maybe he did, and god killed him to keep it a secret. : )
A much more well-known and, to my mind, interesting construct is the Ulam Spiral and the variant Sacks Spiral. Both of these illustrate in much more dramatic detail the concept of primes “regular irregularity,” as Skinner is attempting to illustrate them.
These last two are not errors, but the omissions do make me wonder what else I was missing out on that the author didn’t know about, or didn’t fit in with the theme of his book?
Tomorrow I’ll talk about what I liked in this book.
Sacred Geometry Deciphering the Code |
Pursuant to my interest in the beauty of mathematical ideas, I decided to pick up a copy of Stephen Skinner’s book, Sacred Geometry, which surveys the beauty and synchronicities of whole numbers and geometric concepts. This is a beautify, however somewhat flawed book, and I’ve decided to break my review of it up into two posts highlighting its negative and positive aspects. I like to get the negatives out of the way up front, and leave off with positives. So…
Two Glaring Goof Ups
Da Vinci’s Drawings of the Platonic Solids (Tetrahedron, Hexahedron, Octahedron, Icosahedron, Dodecahedron) |
In the section on the five platonic solids, Skinner notes that the hexahedron (earth) and octahedron (air) are a pair, meaning it’s possible to create one from the other by connecting the vertices to the centers of the faces. Correct, but then he writes that the icosahedron (water) and tetrahedron (fire) are also a pair in this sense, and the dodecahedron (ether) is a pair unto itself; therefore, poetically, ether comes from ether.
Wrong. It’s the icosahedron and dodecahedron that are a pair, each forming the other. I know this because, for a brief phase in my life, I was spending my leisure time getting schnookered and playing with Zome Tools, and have built this association myself. It is the tetrahedron that makes itself; therefore, not quite so poetically, fire comes from fire.
Skinner, like most skips–or doesn’t know about–what I think is the most fascinating aspect of the icosohedron platonic solid: the fact that it is possible to generate three golden rectangles inside it by connecting the vertices. I am so enchanted by this fact, that I keep a ZomeTool model of an icosahedron with the interlaced golden rectangles on my desk at work. It serves as a warning to my geeky coworkers that this desk is my territory:
Ryan’s Icosahedron With Golden Rectangles Highlighted |
Now, as Professor Bender will instruct, ignore the cross lines in the figure, but note the rectangle, which has proportions according to the golden rectangle. Now imagine Dr. Bender rotating the object 180-degrees along the horizontal axis, and the horizontal line will reveal another golden rectangle. A 180-degree twist on the vertical axis, and the vertical line will reveal a golden rectangle. Doesn’t that just make your eyes glaze over with indifference???
Me too. Here’s some good pictures of what I’m talking about. Let’s move on.
When discussing prime numbers, Skinner cites Peter Plichta’s Prime Number Circle, which is titled “Prime Number Cross” in the reference I found, but this is an obscure mathematical construction. I suspect his reasoning for using it is Plichta’s focus on figuring out “God’s Secret Formula” from primes, which he didn’t… or maybe he did, and god killed him to keep it a secret. : )
A much more well-known and, to my mind, interesting construct is the Ulam Spiral and the variant Sacks Spiral. Both of these illustrate in much more dramatic detail the concept of primes “regular irregularity,” as Skinner is attempting to illustrate them.
These last two are not errors, but the omissions do make me wonder what else I was missing out on that the author didn’t know about, or didn’t fit in with the theme of his book?
Tomorrow I’ll talk about what I liked in this book.
