After seeing PZs comments on Stuart Pivar's new version of his book, titled "Lifecode: From egg to embryo by self-organization", I thought I would try taking a look. I've long thought that much of the stuff that I've read in biology is missing something when it comes to math. Looking at things, it often seems like there are mathematical ideas that might have important applications, but due to the fact that biology programs rarely (if ever) require students to study any advanced math, they don't recognize the way that math could help them. So, hearing about Pivar's book, which claims to propose a theory of structural development based on the math describing structural distortions of an expanding figure in a constrained space - well, naturally, I was interested.
So I wrote to the publisher of his book, to see if I could get a review copy. I wanted to try writing a review from the perspective of a mathematician. To my immense surprise, a courier arrived at my door two hours later with a copy of the book! It's a lucky thing I was working from home that day! So I started reading it monday afternoon. I didn't have a lot of time to read this week, so I didn't finish the main text until thursday, despite the fact that it's really quite short.
The book is a spiral bound softcover, about 150 pages long. The print quality is quite poor; it looks like it was photocopied on a standard office copier. (Normally, I wouldn't comment on that in a review, but in this case, much of the content is in the form of diagrams with very fine lines, and in this print-form, the quality of printing is so low that some of the diagrams are quite difficult to see clearly: in places, it's difficult to distinguish between lines that were drawn on the picture, and lines that are an artifact of how it was reproduced.) The remaining hundred pages are reproductions of supporting materials - papers or sections of books by other authors. (To my dismay, nowhere in the text, the credits, the copyright page, does he give any indication that he got permission to reproduce these materials.)
Pivar's theory is that the structure of living things is determined primarily by structural distortion/compression of an expanding body in a constrained space. So, for example, his theory says that the basic bilateral body plan is formed by the compression of a growing toroidal body which is compressed within the form of the original spherical egg - so it's a torus expanding inside of a sphere, and the distortion caused by that results in a crease through the middle, and body forms around that crease line in a bilaterally symmetric form. Genes, in Pivar's theory play a secondary role, at best; he sometimes argues for the irrelevance of genes (if I understand correctly, for the fundamental body plan, he argues that it's dictated by the topological constraints), and he sometimes argues that the physical forces of compression trigger the gene expressions that differentiate between different tissue types (for example, he claims that internal organs are formed by cells differentiating based on the forces that are applied to them by compression through the body structure affecting gene expression).
In order to support this, he does some experiments - taking toroidal plastic tubes filled with fluid, and compressing them in different ways, to show that a toroidal body (which he claims is the fundamental shape of an embryo) compressed in the right way forms the shapes that he argues are the basis of most body plans.
It's an interesting idea.
The problem is, it's wrong.
I don't make a blanket statement like that lightly. The thing is, he comes up with ideas about how various things develop - but he never compares them to how things really develop. There's been a ton of work in embryology and development, which includes detailed descriptions of the forms of the embryo at various stages of development. Pivar's theory says that things develop in embryos in ways that are entirely different from what we observe.
For example, we know that in mammals, the limbs start off as buds, which lengthen, and then new buds form on the end which grow into digits. Pivar argues that this happens by a tube-like structure forming creases, which divide into digits, and then stretch until they break apart into the individual hands or feet. So the two arms form as part of a torus, and then tear into two arms. Nice theory, but experimental observations don't match it. That's just not how it happens.
Most of Pivar's theory is like that. It's stuff which looked at in the abstract is interesting, and which could make an interesting hypothesis. But in science, you don't just stop with an attractive hypothesis, and insist that it's correct because it's such an elegant idea. You need to validate your hypothesis: that is, you test the hypothesis, and see if it works. In fact, you do more than just test it: you do your best to disprove it. If your best efforts don't result in any evidence that contradicts the theory, and other people can reproduce it, and it describes reality better than any other hypothesis, then it may become a viable theory.
Pivar skips the step of validating his idea. He simply asserts that it must be correct, because it's just self-evident that it's right. He's got tons of hand-drawn sketches of how various body plans and physical features could develop using his model of body-form by compression and distortion. He proposed ideas about the development of shells, digits, spider legs, mammalian limbs - none of which match real observations of embryonic development. He argues that a spider's body and legs are formed by topological distortions of a sea-slug like body. But the actual development of a spider from an egg simply does not follow any plan like that. It's just completely wrong.
It's sad, because parts of the hypothesis seems interesting, and there might be something to it. But it's not the be-all end-all theory that Pivar claims it is; and the way that he just blithely asserts things that are in blatant contradiction of facts manages to discredit his ideas in the eyes of the people who could test whether it works on any level. (You can't expect embryologists to take this seriously when it makes such ridiculous errors of fact. It would be like coming to me as a computer scientist claiming to have a proof that P=NP; and as a result of that proof, you can show that general comparison-based sorting takes less than linear time.)
To make matters worse, the text is peppered with off-the-wall criticisms of how foolish the genetic approach is, and blatantly false statements about what genetics predicts, and about what we've been able to learn about how genes influence development.
For example, he repeatedly states various forms of "no code for body-form has ever been found in DNA". But that's not true at all; the HOX genes pattern the body axis, and code for limbs and digits - and they are arranged in clusters that match the arrangement of the body-parts they code for in the organisms body. (See here for a wikipedia article, or here for an article by a professor at the U of Calgary with more details about HOX genes.)
So, on balance... Interesting idea, but it just doesn't hold up to the least bit of scrutiny. It proposes mechanisms for how things develop, which don't match real observation of how things develop. It makes numerous obviously false statements. Even the parts of the argument that appear interesting are woefully incomplete - the entire theory is presented in less than fifty pages including all of the poorly reproduced sketches. And two thirds of the book are reproductions of papers by other authors which do not appear to be reproduced with permission from the original authors. There's just no way that I can recommend this book to anyone.