Quantum Pythagoreans [Paperback]

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"The Pythagorean [one who follows the teachings of Pythagoras, circa 575 BC to circa 495 BC, perhaps best known for his mathematical theorem] central tenet is: ALL IS NUMBER...Pythagorean mathematics deals with the understanding and application of mathematical operations as analogous to the operations of nature...A Pythagorean mathematician does not just describe the behavior of nature. He or she also strives to create what nature creates. A REAL thing is something that was and can be made with numbers through a mathematical and geometric relation...[W]e are going to enter the cave of quantum mechanical shadows, for quantum mechanics [physical theory that describes the motion of objects by the principles of quantum theory] is about things VIRTUAL, things intangible, things altogether frustrating to all who like to think that everything is connected to everything in a predictable and measurable way."

The above is taken from an early chapter of this fascinating book by Mike Ivsin (who holds both technical and business degrees). He is a consultant on computing methods for various applications. Ivsin also has a patent for a "concurrent sorting method."

This is how the first three chapters of this book are laid out. We begin in the real domain with chapter one discussing momentum (the product of the mass of an object and its velocity) and chapter two discussing (star) numbers and operators. (An operator is a term used to indicate that a certain process like multiplication, etc. is to be carried out.) The end of chapter two introduces the reader to the virtual and chapter three (a very interesting chapter!) is dedicated entirely to the virtual domain.

A note on the virtual domain with its virtual particles. Virtual particles are said to exhibit some of the phenomena that real particles do. Many in the scientific community see them as a quantum bookkeeping abstraction that's needed since our current view of reality as described by quantum mechanics is incomplete. Virtual particles may no longer be required when a more complete view of quantum mechanics is integrated with general relativity and gravity in general.

Chapter four is a key chapter that discusses gravitation (the force by which every mass or particle of matter attracts and is attracted by every other mass or particle of matter) in a universe that has both real and virtual domains and as well, allows for "transformations" between these two domains.

At this point, it should be mentioned that the above four chapters are highly scientific in nature. Even though the main narrative defines some scientific words and concepts, some are not defined. Hence these chapters assume some science background especially in physics. Also, chapters 2, 3 and 4 are long, being about 80, 90, and 70 pages respectively. My recommendation is to read these well-written chapters slowly and take frequent breaks or else you will get lost in a mass of scientific detail.

It should also be mentioned that this book, despite the word "quantum" in the book's title, deals with the universe on both the atomic and cosmic scales.

Chapters five, six, and seven (the final chapter) have less science and thus are much easier to read than the preceding four chapters but only if you have comprehended the major ideas of the first four chapters.

Chapter five was a pivotal chapter (at least for me). I enjoyed this chapter since it was written so well. It has the author coming across "a structure that did not look like a real house." He also has strange encounters with the inhabitants who live inside this house. If you have read chapters one to four carefully, you should have no trouble understanding this chapter.

The penultimate chapter is a helpful chapter since it puts all the previous chapters in perspective by explaining real, virtual, and the real & virtual working together. As well, it introduces some new information. The last two sections discuss the real and virtual inside the brain--a fascinating discussion!

The final chapter alters the biblical seven days of creation found in Genesis to five days. I should mention that the author has hinted briefly at an intelligence or a creator in his preceding chapters. In this chapter, he just assumes there is a creator (there is no discussion as to why there is one) calling the creator at key points "the Magician." In fact, the author has a discussion with the creator throughout this chapter. At the end of each day is a summary (in boldface type) of what was accomplished. For example, here is part of what is printed in boldface for day five:

"On the fifth day the Magician created the human in the image of both the real and the virtual domains of the universe."

Throughout the main narrative you'll meet key thinkers of the past (besides Pythagoreans) such as Galileo, Kepler, and especially Sir Isaac Newton. Diagrams are peppered throughout to help you understand important concepts. (These are especially helpful in the science chapters.) As well, there are interesting and informative footnotes throughout (with no awkward notes at the end of the book).

An appendix is included at the end. It details fifteen important concepts. Especially helpful here is the "Classification of numbers" table. I found most illuminating the section entitled "Some geometric relations of The Great Pyramid."

Finally I had only one problem with this book: there is no index. I couldn't understand this since it is jam-packed with information and is so well laid out. Especially frustrating for me was when I wanted to refresh my memory of a key definition. I had no choice but to meticulously search the pages I had read and hope I stumbled on the definition that I was looking for. Thus I recommend that the potential reader note the page number locations of key definitions and concepts. (This is especially good advice for the science chapters.)

I also feel that a glossary would have been helpful for the potential reader. It should have included not only words and concepts defined in the main narrative but also included words and concepts not defined in the main narrative.

In conclusion, you may not agree with everything you read in this book but it certainly engages the reader from the organization and self-organization perspectives!!

(copyright 2006; 7 chapters; main narrative 335 pages; appendix; bibliography)

<<Stephen Pletko or "Uncle Stevie," London, Ontario, Canada>>

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Mike Ivsin has written a book that challenges current thinking about the nature of matter. And while the author is thoroughly familiar with theories put forth by modern physicists to explain the weirdness of our universe, he reaches back in time to the creative and often misunderstood ideas of Pythagoras, a Greek who lived circa 500 BC, and who gave his name to the Pythagorean Theorem. But Pythagoras was much more than a dabbler in mathematics; he saw numbers as key to the understanding of everything and he founded a mystical school whose teachings were imparted in secret to initiates. His greatest influence was on the study of geometry and his symbol was the ten-dot tetractys

You'll get plenty of new ideas about geometry in this book. Especially fascinating is the information on planetary movement forming geometric shapes, and the results obtained when you combine the orbits of more than one planet (for instance Venus-Earth). In turn, these relate to the musical scale. It seems the "music of the spheres" is encoded into our universe in mathematical relationships.

If numbers are the key to understanding, then one must understand numbers. In this book, you'll learn about those numbers now called "irrational" but called "unspeakables" or "incommensurable" by Pythagoreans. The "transcendentals" are numbers that cannot be written, as they would be of infinite length. Some irrationals represent shapes that have special meaning for human consciousness. For instance, irrational numbers form the Golden Ratio (1.61.. to 1) used since ancient times in formal architecture that is especially pleasing to the eye. The Great Pyramid incorporates this ratio and, interestingly, it is also frequently found in nature (seashells, pinecones, etc.).

Applied to musical notes, some irrationals are pleasing and some not, but all are incredibly rich in timbre, for they belong to the virtual world. Pythagoreans believed numbers come alive when they manifest in objects, but irrationals cannot be expressed with mathematic precision in the material world. Irrational numbers are intractable, which Ivsin equates with being not computable. Even a supercomputer cannot calculate intractable numbers, and simulations soon become inaccurate.

Plato was a Pythagorean who founded a school that lasted 900 years. He attempted to explain the mystery of dual realities by a metaphor. The Cave of the Shadows was a theoretical place where prisoners had to learn of objects, not by seeing the thing itself, but by seeing its shadow. When faced with the real object, how would they regard the shadow?

Reality, we learn, is dual - real and virtual, or, one could say, visible and invisible. Both electrons and light are particles that can spread and become virtual. Free electrons pass easily from real to virtual, their energy transformed into "vivibration" (virtual energy). Is the virtual world the world of irrational numbers? Where do electrons go when the waveform collapses?

In this book you will learn about hyperstates based on mass, force and distance, each with the possibility of zero to three degrees of independence. This is complicated, but the book provides illustrations and tables that help clarify the concepts.

Throughout the book, there are small poems, quotations and stories. Some seem a bit mysterious, but that is the point. Reality is mysterious and understanding does not come only from looking at equations. Mike Ivsin skillfully weaves in these snippets as well as imaginary conversations with Newton and, at the end of the book, with the Creator. Throughout the book are tantalizing tales from the lives of the sages who shaped our modern ideas about the universe. We meet Euclid, Plato, Newton, Kepler, Planck, Schrodinger and many others during this journey that begins with the meaning of momentum and ends with an understanding of balance between real and virtual reality.

The author is highly critical of some of the ideas that have become accepted by modern physicists. He does not believe in black holes and he does not believe light can exert pressure on a mirror. He is adamant that experiments could prove that light is virtual (meaning it cannot exert pressure) if only scientists would do the experiments. Ivsin weighs in on the double-slit experiment and other milestones of physics, providing fresh ideas about the concepts that have shaped current thinking about the nature of reality.

This is not your usual book about physics. It is filled with original and thoughtful ideas, blended with ancient ideas that have survived and continue to reveal hidden meaning. You may agree or disagree with this modern Pythagorean, but on every page you will be challenged.