Proving Darwin: Making Biology Mathematical

by Gregory Chaitin

Groundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin’s theory of evolution works on a mathematical level.
 
For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has even attempted to answer it until now.
 
In this illuminating and provocative book, Gregory Chaitin argues that we can’t be sure evolution makes sense without a mathematical theory. He elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Chaitin presents an accessible introduction to metabiology, a new way of thinking about biological science that highlights the mathematical structures underpinning the biological world. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.

Genres: Science, Biology, Evolution, Nonfiction, Mathematics, Philosophy, Computer Science

144 pages, Hardcover

First published January 1, 2012

About the author

Gregory Chaitin is widely known for his work on metamathematics and for his discovery of the celebrated Omega number, which proved the fundamental unknowability of math. He is the author of many books on mathematics, including Meta Math! The Quest for Omega. Proving Darwin is his first book on biology. Chaitin was for many years at the IBM Watson Research Center in New York. The research described in this book was carried out at the Federal University of Rio de Janeiro in Brazil, where Chaitin is now a professor. An Argentine-American, he is an honorary professor at the University of Buenos Aires and has an honorary doctorate from the National University of Cordoba, the oldest university in Argentina.

Reviews

[Brandon · Rating 2 out of 5]

(Taken from my review of this on Amazon and modified)

I bought this book because I thought it would be interesting to see a mathematical model of evolution. In DARWIN'S DANGEROUS IDEA: EVOLUTION AND THE MEANINGS OF LIFE , Daniel Dennett proposed that evolution was an algorithmic process. I believe that he is correct, so when I saw a book claiming that evolution could be modeled and proven to be inevitable by mathematics, I was excited.

However, this book is not written by someone knowledgable of evolutionary biology. As such, the model of evolution presented here does not really describe the random mutation followed by natural selection discovered by Darwin & Wallace and later evolutionary biologists.

The reason for this is his view of evolution is not the atheistic-naturalistic view. He is a self-admitted Pythagorean who views the ultimate nature of reality not as material, but as mathematical. He does reject Platonic dualism and is a monist, but he thinks that this "material" world is just one aspect of a mathematical multiverse. He identifies with Leibniz, Spinoza, Pythagoras, and Plato philosophically more than the likes of Aristotle, Locke, and other empiricists. This is typical of mathematicians to have a very Platonic-Pythagorean worldview, which I think is a hazard of the job when you work with numbers for a living. Of course, in order to view mathematics as the fundamental constituents of reality, one must also grant numbers ontological status. I have a much more pragmatic view of numbers, that they are mere place holders for what could be, and that the rest are just useful abstract concepts. For instance, 2+2=4 could be a place holder for any two objects added to two more objects. The numbers have no independent ontological status of their own.

The reason for the two stars is not for my philosophical disagreements with the author, but for his lack of real understanding of evolutionary theory (-1 star), the tenacity to claim to have mathematicaly proven evolution when he doesn't seem to truly understand biology itself (-1 star), and the quality of the writing.The book was very short and has the feel of a bunch of collected blog posts. He improperly uses and over uses ellipses (...) and the sentences are very choppy. He also lazily used a transcript of one his lectures as a chapter.(-1 star). The two stars he does have are earned for the attempt at modeling evolution which is something that I do think will be worthwhile to do, and one star out of generosity.

However, if you are wanting to read this book it is probably not worth reading. If you want to understand evolution, I recommend What Evolution Is ,The Greatest Show on Earth: The Evidence for Evolution , and Wonderful Life: The Burgess Shale and the Nature of History . To understand the origins of life, I recommend What Is Life?: How Chemistry Becomes Biology . To understand how the most basic life forms work, I recommend Wetware: A Computer in Every Living Cell and The Machinery of Life . For a debunking of the teleological view that Chaitin presents of evoluton -- he claims evolution is inherently creative and goal oriented which is precisely what makes his model non-Darwininan -- read Full House: The Spread of Excellence from Plato to Darwin .

[Michael Jandrok · Rating 4 out of 5]

Mathematician Gregory Chaitin attempts to provide a mathematical model of evolution in this short book based on a university course given in the Spring of 2011 at the Federal University of Rio de Janeiro, where the author is a professor. It also adapts material given at one of his lectures at the Santa Fe Institute. It is a quick read and an outline at best of his work, but it does give the reader a general idea of the concepts behind what the author calls "metabiology," an attempt to model evolutionary adaptation through computer software rather than natural software, otherwise known as DNA.

The central premise of this book is that by utilizing algorithmic information theory and the flexible and creative nature of postmodern mathematics, one can construct a working mathematical toy model of evolution, creating a piece of randomly mutating software that selects for a fitness trait. The main idea here is that DNA is a naturally occurring piece of software, our internal programming language as it were. This is not an original concept, but it is one that Chaitin expands upon greatly in the text.

I'll admit that it's an absolutely compelling idea. Evolution, after all, is the backbone of modern biology, but its main concepts are often misunderstood or outright rejected by a significant portion of the population. If one can really take a mathematical model and "prove" that the basic mechanisms of evolution (random mutations and natural selection) work as advertised, then it could go a long way towards advancing scientific literacy.

Keep in mind that the author's model is simplistic at best, selecting for only one trait and having none of the environmental pressures that truly drive adaptation. That said, it DOES work, and it provides a foundation for more complex models that will more thoroughly mimic life processes in the future, especially as biotechnology advances into computer science.

There ARE mathematical formulas presented in the text, but they don't overshadow the main ideas. You'll probably understand most of the general ideas if you have a basic proficiency in high school level algebra and/or logic. The appendices go into additional technical detail, but they can be skipped unless you have the educational foundation to fully understand the concepts presented.

I'd recommend this book to anyone with an interest in the subject matter, though I would like to see an expanded and more accessible revision of this work at some point in the future.

[DrosoPHila · Rating 1 out of 5]

A quick glance at the references are enough to pick up big problems with this work. A well-referenced book might lie anywhere on the awful-amazing spectrum, but a badly-referenced book is inevitably awful because it reveals that the author simply hasn't thought through his thesis.

Anyone needs to do sufficient background reading before claiming to be knowledgeable - but especially when it is outside your field of training (in the author's case, mathematics). This would, I contend, be rather more than an assorted collection of half a dozen popular science books (which by their nature tend not to be particularly mathematical), which Chaitin references for further reading.

Secondly, one should always submit technical ideas to appropriate places such as a the peer-reviewed Journal of Theoretical Biology where it will be peer-reviewed by experts in the field, and then published (or ignored as the case may be) on its merits. A self-published book (which will tend to be ignored by the scientific community) is not the place for this.

The author has apparently done neither. If he had done the first, he would have discovered the wonderful (if sometimes headscatchingly confusing) world of mathematical biology, and avoided potentially duplicating previous work. Had he done the second, he wouldn't have written this book in the first place.

Footnotes:
1. Quite how for example one manages to cite John Maynard Smith's popular treatise The Theory of Evolution , but ignores the same professor's Mathematical Ideas in Biology and Evolution and the Theory of Games , and too many papers on related subjects to list here, is beyond me.

2. Similarly, how one can read and then cite Richard Dawkins' The Blind Watchmaker , yet miss his more important contributions The Selfish Gene and The Extended Phenotype . Any serious reading of Watchmaker should have really turned the author away from the erroneous view that evolutionary biology is open to serious doubt and therefore in need of his "mathematical proof" - yet the way he references it implies that he thinks that Dawkins said the exact opposite.

This is just shoddy scholarship.

[Francisco Barrios · Rating 1 out of 5]

Este libro me parece una profunda decepción de lo que era para mí el autor (el libro Meta Math! The Quest for Omega (2005) me pareció brillante), así como de la colección Metatemas de Tusquets. Probablemente algún editor "new age" creyó que este era un buen lugar para publicarlo en español (al lado de Schrödinger y Mandelbrot, por ejemplo), pero la verdad es que este libro queda a deber por malo.

Y no cuestiono los alcances o el análisis (profundo, sin duda) que hace Chaitin de la Biología como una ciencia que trata de la información; sino que estoy en contra de que algunos autores armen un libro de divulgación alrededor de una conferencia (o artículo) y rellenen con detalles banales los intersticios, apelando a que si "[m]i amigo Stephen Wolfram tiene libros de teología de Newton y Leibniz (originales, no copias) de trescientos años de antigüedad, colocados unos junto a otros en un estante" (p. 45), o bien que "[v]eamos algunas observaciones relacionadas con esto procedentes de mi herencia cultural judía" (p. 112) o un extraño reclamo a los "reduccionistas" que apelan a una matemática alejada de los credos particulares de los científicos (p. 108). Aspectos todos que no abonan a ninguna de las tesis fundamentales de la obra.

El título mismo es engañoso: "Demostrando a Darwin. La biología en clave matemática". No. Lamentablemente asisitimos a un despliegue de ciencias de la complejidad informática que toma una definición de "vida" no exenta de polémica y muestra que, matemáticamente, existe un objeto que cumple dicha definición. Si la definición de marras es una que da mucho peso a las mutaciones genéticas para adaptarse al medio, entonces la "demostración de Darwin" (según el autor) se sigue de ver que existe un objeto que cumple con la definición.

Sin embargo, tal vez el propio Chaitin ignora que la selección natural (como la planteaba el propio Darwin) no apelaba a las mutaciones genéticas o que, desafortunadamente para él, Charles Darwin no leyó a Watson ni a Crick. Pero en tiempos de la posmodernidad ¡estos y otros pecadillos no importan para dar a las prensas una obra con anacronismos, digresiones irrelevantes, un tono desigual, e ignorancia de la historia y la filosofía de la ciencia!

Lamentable.

[Davut · Rating 4 out of 5]

The writer divides the mathematicians into two as one is the theoreticians the other is the problem solvers. This book is a good example of constructing a theory behind the mutations and improvements of the genome sequence from a theoritician point of view. It is a good and easygoing book that attracts me as i wished to have the possibility to work on it in details.

[Walter Alini · Rating 3 out of 5]

Un paralelo entre el ADN y el software, para introducir la metabiología.
Interesante como introducción, pero creo que queda en el medio del mundo del no científico (que no entenderá el trasfondo de la cuestión) y el mundo del científico (que no verá satisfecha su curiosidad).

[Dale · Rating 1 out of 5]

Why, oh why, do people with little background in biology and evolution feel compelled to write books about evolution? It's a dark mystery.

[Chris Aldrich · Rating 2 out of 5]

This book combining biology, microbiology, mathematics, evolution and even information theory is directly in my wheelhouse. I had delayed reading it following a few initial poor reviews, and sadly I must confirm that I'm ultimately disappointed in the direct effort shown here, though there is some very significant value buried within. Unfortunately the full value is buried so deeply that very few, if any, will actually make the concerted effort to find it.

This effort does seem to make a more high-minded and noble attempt than what I would call the "Brian Greene method" in which an academic seemingly gives up on serious science to publish multiple texts on a popular topic to cash in on public interest in that topic through sales of books. In this respect Chaitin is closer to Neil deGrasse Tyson in his effort to expound an interesting theory to the broader public and improve the public discourse, though I would admit he's probably a bit more (self-)interested in pushing his own theory.

Though there is a reasonable stab at providing some philosophical background to fit the topic into the broader fabric of science and theory in the later chapters, most of it is rather poorly motivated and is covered far better in other non-technical works. While it is nice to have some semblance of Chaitin's philosophy and feelings, the inclusion of this type of material only tends to soften the blow of his theoretical work and makes the text read more like pseudo-science or simple base philosophy without any actual rigorous underpinning.

I'm assuming that his purpose in writing the book is to make the theories he's come up with in his primary paper on the topic more accessible to the broader community of science as well as the public itself. It's easy for a groundbreaking piece of work to be hidden in the broader scientific literature, but Chaitin seems to be taking his pedestal as a reasonably popular science writer to increase the visibility of his work here. He admittedly mentions that his effort stems from his hobby as his primary area is algorithmic information theory and computer science and not biology or evolution, though his meager references in the text do at least indicate some facility with some of the "right" sources in these latter areas.

Speaking from a broad public perspective, there is certainly interest in this general topic to warrant such a book, though based on the reviews of others via Amazon, Goodreads, etc. the book has sadly missed it's mark. He unfortunately sticks too closely to the rule that inclusion of mathematical equations is detrimental to the sale of ones books. Sadly, his broader point is seemingly lost on the broader public as his ability to analogize his work isn't as strong as that of Brian Greene with respect to theoretical physics (string theory).

From the a higher perspective of a researcher who does work in all of the relevant areas relating to the topic, I was even more underwhelmed with the present text aside from the single URL link to the original much more technical paper which Chaitin wrote in 2010. To me this was the most valuable part of the entire text though he did provide some small amount of reasonable detail in his appendix.

I can certainly appreciate Chaitin's enthusiastic following of John von Neumann but I'm disappointed in his lack of acknowledgement of Norbert Weiner or Claude Shannon who all collaborated in the mid part of the 20th century. I'm sure Chaitin is more than well aware of the father of Information Theory, but I'll be willing to bet that although he's probably read his infamous master's thesis and his highly influential Bell Labs article on "A/The Mathematical Theory of Communication", he is, like most, shamefully and wholly unaware of Shannon's MIT doctoral thesis.

Given Chaitin's own personal aim to further the acceptance of his own theories and work and the goal of the publisher to sell more copies, I would mention a few recommendations for future potential editions:

The greater majority of his broader audience will have at least a passably reasonable understanding of biology and evolution, but very little, if any, understanding of algorithmic information theory. He would be better off expounding upon this subject to bring people up to speed to better understand his viewpoint and his subsequent proof. Though I understand the need to be relatively light in regard to the number of equations and technicalities included, Chaitin could follow some of his heroes of mathematical exposition and do a slightly better job of explaining what is going on here. He could also go a long way toward adding some significant material to the appendices to help the higher end general readers and the specifically the biologists understand more of the technicalities of algorithmic information theory to better follow his proof which should appear in intricate glory in the appendix as well. I might also recommend excising some of the more philosophical material which tends to undermine his scientific "weight." Though I found it interesting that he gives a mathematical definition of "intelligent design", I have a feeling its intricacies were lost on most of his readership -- this point alone could go a long way towards solidifying the position of evolution amongst non-scientists, particularly in America, and win the support of heavyweights like Dawkins himself.

I'll agree wholeheartedly with one reviewer who said that Chaitin tends to "state small ideas repeatedly, and every time at the same shallow level with astonishing amount of redundancy (mostly consisting of chit-chat and self congratulations)". This certainly detracted from my enjoyment of the work. Chaitin also includes an awful lot of name dropping of significant scientific figures tangential to the subject at hand. This may have been more impressive if he included the results of his discussions with them about the subject, but I'm left with the impression that he simply said hello, shook their hands, and at best was simply inspired by his having met them. It's nice that he's had these experiences, but it doesn't help me to believe or follow his own work.

For the technically interested reader, save yourself some time and simply skim through chapter five and a portion of the appendix relating to his proof and then move on to his actual paper. For the non-technical reader, I expect you'll get more out of reading Dawkins' early work (The Selfish Gene) or possibly Loewenstein's The Touchstone of Life.

Though I would certainly agree that we could use a mathematical proof of evolution, and that Chaitin has made a reasonable theoretical stab, this book sadly wasn't the best one to motivate broader interest in such an effort. I'll give him five stars for effort, three for general content, but in the end, for most it will have to be at most a 2 star work overall.

[Jerzy · Rating 1 out of 5]

Information theory and computer science aren't my field, so I have only a little to say about the content.
But I have more to say about the presentation :)

Content:
The toy model he presents strikes me as (1) not novel, and (2) not rich enough to found a whole new field, and (3) not relevant enough to real-world constraints to draw the conclusions he does.
(1) Plenty of people have played with computer simulations of evolution and with mathematical abstractions of such simulations. Maybe his specific model really is new, but the broader idea isn't.
(2) Maybe you could go back and find all these pre-existing models and call *that* a new sub-field within biology. But it's ballsy to propose one model all by yourself (OK, together with his wife, that's actually kinda sweet) and then claim it deserves status of an entirely new field (not even a sub-field), on par with biology or mathematics.
(3) His model assumes there are oracles which can tell you, immediately, which programs do and don't halt. There are good uses for such oracles in computational/mathematical theory, e.g. to bound the ideal (but unattainable in practice) best/worst case performance of your model. But if you assume such oracles to get a bound you know is unattainable in practice---then you have to be careful in drawing connections to the reality of biology/evolution, where there are time & resource constraints and such oracles don't exist. It's fine to build a simple toy model, but you have to have humility about its relevance, and there's not much humility here.

Ad hominem attacks:
* As exemplars of courage and creativity, he lists people who started their own journals because no one else would publish their pet theory (such as cold fusion). To me, that connotes desperation and futility, not maverick independence.
* If it's not enough to make grandiose claims about biology, he also draws grand implications about theology and politics! Again, this is based on a loose sketch of a toy mathematical model with no clear link to anything in reality.
* After shouting that our society must encourage creativity, he cites as a positive example his Jewish heritage, where "every male is supposed to study." I know nothing about *actual* Jewish educational traditions. But the way he *describes* it here, "every male" sounds like "no girls allowed" which doesn't strike me as a pinnacle of openness and creativity.
* His attempts at humor and enthusiasm come off as condescending: "After all, the world must be made out of something, and we certainly can't use marshmallows!"

All in all, he comes across as a complete crank.
It reminds me of Stephen Wolfram (see Cosma Shalizi's lovely review), whom he mentions as a friend.

Edit: But I really love the von Neumann quote in the appendix:
"So far I have been rather vague and confusing, and not unintentionally at that."

[Andrew · Rating 2 out of 5]

This book promised so much, and yet delivered so little. To be sure, the author has some very interesting ideas that are worth being exposed to but that does not save this book. The first problem is in delivery - almost the entire book seems to be taken verbatim from class lectures. Certain content is duplicated often enough, that the book could have been cut in half with no loss. The second issue lies in the content itself. The author claims to have developed a working toy model of Darwinian evolution. But there's one fundamental problem here - his model relies on algorithmic mutation to introduce diversity, whereas real organisms generally undergo bitwise mutation. Hence, his model allows for a much more sophisticated search of the genotype space than is allowed in nature. In the same vein, by his own admission, the model can not actually be simulated, because it relies on a fitness function that can not be guaranteed to produce a result.

Not as important, but still misleading, is that his result claims to model Darwinian evolution. This is not true, as Darwinism posits that all existing life forms came into being from nothing (or from a primordial soup, if you wish) solely through natural selection acting on genetic crossover & mutation. What his model actually demonstrates (or would, if it could be simulated) is non-Darwinian adaptation & evolution. His evolution is only capable of tiny incremental changes that can not possibly create entirely new structures - they can only rearrange existing structures.

In summary, the fundamental ideas relating biology-mathematics-creativity are very interesting, as is the goal of developing a mathematical model for evolution. However, all this is worth a 30-60 minute lecture; not this book.

[Wj · Rating 1 out of 5]

So far - yes, I'm in chapter 2 but the book is already starting to - look bad.

As thin as the book is, it constantly manages to state small ideas repeatedly, and every time at the same shallow level with astonishing amount of redundancy (mostly consisting of chit-chat and self congratulations).

Meanwhile, a number of snobbish self-celebrating side notes have been sprinkled here and there, such as how the author (and maybe his good friend some big name) have collected some ancient books by Newton.

Above all, it seems the author considers the great theory (that a math model can be derived for evolution, and life / DNA = software) presented in the book is as important as Newton's law. By the depth of it, it seems laughable from both sides: serious biologists and serious computer scientists.

[Katherina · Rating 1 out of 5]

Wow. I've only skimmed through a dozen pages and all I've noticed are the numerous exclamation points.
That just doesn't strike me as a convincing literary piece.
I picked the book up because of the title, thinking it would actually go in depth with the theory, but only reading the first two chapters I am disappointed with this book and I wouldn't even bother reading it.

[Eric · Rating 2 out of 5]

Proving Darwin: Making Biology Mathematical actually takes a small but important part of biology, DNA as information which can mutate at random, and applies algorithmic information theory, to which Chaitin contributed some fundamental results, to make the case that biology can be given a rigorous mathematical foundation. Other parts of biology, like population dynamics, physiology, and natural selection, are dismissed as minor details. Even in his restricted domain, Chaitin glosses over most of the details and makes pronouncements which even mathematically sophisticated readers would be hard pressed to verify. (In Appendix 2: The Heart of the Proof, Chaitin just offers a sketch of his proof, although he claims that it would be "... a routine matter for anyone with an expert knowledge of algorithmic information theory to complete the proof." Not helpful.) Additionally, Chaitin sprinkles far too many exclamation points throughout the book, which makes his arguments seem suspect. Although the book appears to be written for a general audience, the math is both too special and not specific enough to allow the non-specialist to judge its merits.

[Julianna Crisanti · Rating 1 out of 5]

This book is useless disorganized drivel in need of heavy editing. Not only does he meander between points, not really focusing and expanding on one at a time, the author references works of other scientists and mathematicians at an alarming volume per page. It also seems as an outlet for the author's ego as he constantly boasts about his connections and possessions. I would say a good 30% of this book is either randomly boldfaced or a reference to the "climax" of the book, Chapter 5 (his lecture). Furthermore, his persistent use of enthusiastic colloquial phrases ending in exclamation points made me cringe every time. Needless to say, I'm glad I only spent $2 on this piece crap that I found on a clearance shelf at Half Priced Books.

[Mark Isaak · Rating 3 out of 5]

This is not a biology book. Chaitin develops a proof that evolution can happen, but his model is so different from biological life that its applicability to the real world is far from apparent. The writing itself is amateurish, with name dropping, redundancy, misuse of ellipses, and lots and lots of exclamation points. The main value of the book, in my opinion, is that it gives a good idea of how a mathematician thinks, breaking a problem down into abstractions that can be dealt with in equations. Whether or not Chaitin's proof, or his whole concept of metabiology, will lead to anything productive remains to be seen.

[Jeff Grant · Rating 2 out of 5]

Meh. It wasn't very entertaining and lacked examples to bring me in more. I was excited initially to look at evolution through a stronger mathematical lens but this book did not keep my interest. He had a lot of valid points but I feel I have already learned a lot about random walks in statistics so his lecture lacked umf for me. If you haven't though about probability linked to evolution this book may give you a heads up.

[Chelsea · Rating 2 out of 5]

Entertaining read, but that was about all it had going for it. The ideas didn't provide any particularly interesting insights and it was obvious that the author was a mathematician who was trying to apply his area of expertise to an area he knew little about (evolutionary biology). Many times he demonstrated a fundamental lack of knowledge about basic biological concepts, or dismissed central ideas as irrelevant in order to make his proposal appear viable.

[Perry · Rating 4 out of 5]

I'd be lying if I said I understood the math being portrayed in this book. I was hoping it would dumb it down enough for even me to understand, but my confidence in my math skills has eroded since high school. There are some intriguing elements in the parallel between genetics and computer science, but the addition to faith to the equation left me incurious. The book has made me curious about Von Neumann, so maybe I'll see where that leads me.

[Natalia Fredes · Rating 2 out of 5]

La idea de una teoría de la evolución, matemáticamente demostrable suena llamativa y muy prometedora. Sin embargo, en el libro se hacen algunos supuesto de acerca de biología de poblaciones, y de progreso evolutivos que realmente carecen de sustento. Finalmente, en cuanto a la narrativa es muy repetitivo, mencionando una y otra vez los mismos argumento.

[Grzegorz · Rating 2 out of 5]

The book promises a lot and delivers very little. The main idea is nice, but the exposition is definitely lacking...

It's kind of amazing that in such a short book the author is able to fill at least 50% of the content with his own ego. There are numerous mentions of famous people that Chaitin met and even a passage about rare books that his famous friend Wolfram owns. :)

[Andrés Sebastián · Rating 4 out of 5]

Un paper explicado mostrando como matematicamente la evolución darwineana funciona. Muy interesante y sobre todo inspiracional, pero por momentos difícil de entender. Creo que habla desde un background de conocimiento muy profundo del tema y las dificultades de la teoría de la evolución, pero no logra contextualizar todo lo bien que se podría el tema, en mi opinión

[Sophie]

currently reading because i impulse bought in seekers on the day we were watching the matrix in my students world religion class and neo saw through reality to the code and I was like, oh ya, remember when I thought I was the world expert on popular science books that explains algorithms. I guess I better give this one a go. so far unsure

[L-ssar · Rating 1 out of 5]

Repetitivo, inconexo y no aporta nada.

[Benji · Rating 4 out of 5]

'Cumulative random evolution is much closer to intelligent design than it is to brainless exhaustive search.'

[Edgar Rivera · Rating 5 out of 5]

Conocí a otros excelentes e interesantes libros que me encantaría leer

[Laurel · Rating 5 out of 5]

I loved this but my area of expertise is Turing's 1936 paper so niche read.

[Douglas Summers-Stay · Rating 3 out of 5]

Despite the title and the cover image, this isn't an anti-creationist screed. Chaitin is interested in showing that it is possible for evolution to be genuinely creative, producing new information about the environment that can't be derived from the information already in the genes. To do this he abstracts the problem and considers evolution of algorithms by making random changes to the bits of the program. He shows that by randomly walking through the space of programs, keeping those changes that make progress on the busy beaver problem, and with the use of an oracle telling which programs will halt, one can gain more and more of the bits of omega.
The busy beaver problem is the problem of finding which algorithms take the most steps to finish, but do eventually finish. The oracle is needed because how do you know whether a program never finishes, or just hasn't finished yet? You basically need to do a mathematical proof about what is being calculated. This is the "halting problem." And omega is a little harder to explain. It's a number like pi, a real, irrational number, that encodes in its digits all of the axioms of mathematics. If you want to know more than that you'd probably better read some of Chaitin's other writings (there's a lot of stuff online.)
I felt like the book was disjointed, and his speculations didn't build up into a larger insight about the ability of evolution to come up with creative solutions. Also it was very, very short.

[Jessada Karnjana · Rating 5 out of 5]

สิ่งที่ Chaitin พยายามจะทำ หรือบอกคนอ่านว่าพยายามจะแสดง ถูกเขียนผ่านชื่อรอง Making Biology Mathematical แต่ในความเห็นของผม ผมว่าไม่ประสบผลสำเร็จนัก เพราะสิ่งที่แกเสนอ ยังเป็นแค่ก้าวเริ่มต้น ยังไม่ใช่การพิสูจน์ และยังไม่ถูกทำเป็นคณิตศาสตร์ (อย่างน้อยก็ในมุมมองแบบเก่า ซึ่งแกว่าไม่พอเพียงที่จะนำมาใช้งาน) อันที่จริงแล้ว สิ่งที่แกทำคือ simulation สิ่งมีชีวิตโดดเดี่ยวตัวหนึ่ง คือ นักคณิตศาสตร์ ในเอกภพเล็ก ๆ แล้วบอกว่านักคณิตศาสตร์ตัวนั้นสามารถวิวัฒนาการได้อย่างไม่สิ้นสุด ซึ่งสิ่งที่ใช้วัดวิวัฒนาการคือความสามารถในการแก้ปัญหา Busy Beaver นักคณิตศาสตร์จะต้องส่งมอบคำตอบคือจำนวนเต็มบวกที่ใหญ่ขึ้นใหญ่ขึ���นในทุกรอบของวิวัฒนาการ (ซึ่งแน่นอนว่าวิธีการสร้างคำตอบที่ดีกว่า N นั้นมีอยู่นับไม่ถ้วน เช่น N+N, N*N, N^N, ...) ตามความเข้าใจของผมนะ ถ้าคุณคุ้นเคยกับ evolutionary algorithm (เช่น genetic algorithm) ใน AI ไอเดียของ Chaitin ก็คล้าย ๆ กัน ข้อแตกต่างคือ สิ่งที่วิวัฒนาการใน EA คือ ประชากร ซึ่งเรามองเป็น vector ที่อยู่ใน solution space, และ vector ตัวที่อยู่รอดคือตัวที่ทำให้ cost function ต่ำสุด แล้วสืบทอดสมบัติบางอย่างให้กับรุ่นถัดไป ขณะที่สิ่งที่วิวัฒนาการของ Chaitin คือตัวนักคณิตศาสตร์เองซึ่งเป็น algorithm นั่นคือ ถ้าเราเอานักคณิตศาสตร์ของแกทุกรุ่นมามองรวมกัน เท่ากับเรากำลังมอง algorithm space แกบอกว่าแกทำให้ algorithm (นักคณิตศาสตร์) กลายพันธุ์ แล้ว algorithm ที่กลายพันธุ์เพื่อส่งมอบคำตอบที่ดีกว่าคือ สิ่งมีชีวิต (ในภาพรวม มันก็คือ hill-climbing random walk) โดยอ้างนิยามสิ่งมีชีวิตของ Maynard Smith กับ Szathmáry, ทีนี้ ถ้าเราไปทำให้เกิดการกลายพันธุ์ที่ algorithm มันก็หลีกเลี่ยงไม่ได้ที่ ใน algorithm space จะที่มี algorithm ที่เราไม่สามารถบอกได้ว่ามันไม่มีทางทำงานเสร็จหรือมันยังทำงานไม่เสร็จ แกจึงต้องพูดถึง halting problem และเอาเจ้า Oracle ของ Turing ใส่เข้าไปในเอกภพของแกด้วย เพื่อให้ไม่มีนักคณิตศาสตร์ halting และความคิดสร้างสรรค์เชิงคณิตศาสตร์ไม่ถูกจำกัด (ในแง่หนึ่ง oracle จึงเป็น source ของความคิดสร้างสรรค์) เพื่อเสริมน้ำหนักในเรื่องนี้ Chaitin ก็ยก Emil Post ที่พูดถึงทฤษฎีบทความไม่สมบูรณ์ของเกอเดลว่าเป็นสิ่งสะท้อน creativity ในคณิตศาสตร์เข้ามาเทียบเคียง แล้วเดินสู่ข้อสรุป "biology creativity = math creativity" มีข้อน่าตื่นเต้นประการหนึ่งเป็นผลสืบเนื่องคือ เราไม่ได้วิวัฒนาการเข้าสู่อะไร และ sex ไม่ใช่การส่งให้ข้อมูลบางอย่างอยู่รอด ฉะนั้น มันไม่ selfish, แกเปรียบเทียบว่า คุณจะเรียกคนที่โยนสมบัติหรือเงินทิ้งไปครึ่งหนึ่งว่าเห็นแก่ตัวได้เหรอ (พูดตัวอย่างนี้ซ้ำอย่างน้อยสองครั้งในหนังสือ) แต่ sex เป็นกลไกของ creativity และสุดท้ายแล้ว ไม่มีอะไรที่อยู่รอด ... Πάντα ῥεῖ ...

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[Alex Nelson · Rating 3 out of 5]

I'm no biologist, but I am familiar with Chaitin's work in mathematics.

As per the writing style, it's smooth and written conversationally. It's as though he were discussing his work at the dinner table. Consequently, it's great for me (a mathematician, not a biologist).

Now, regarding the beliefs Chaitin espouses. I find his take interesting. Ultimately, Chaitin argues DNA is the important thing in life, and life is marked by evolution.

He then pursues the standard machine learning approach to things, considering a random walk in an infinite-dimensional space. This I understand and am mildly fine with.

However, I suspect the physical/chemical aspects to cells necessitate their life cycle. But one could meaningfully model this at a higher level of abstraction than the "follow-your-nose" biophysical approach. (Something like Ron Maimon's preprint on the computational theory of biology.)

Consequently, given that belief, I find it hard to digest Chaitin's argument that DNA is all that matters, and the biophysics are a distraction.

I think something in the middle is true, and dismissing biophysics so easily overlooks some critical aspects to life.

[Devero · Rating 3 out of 5]

In se è una lettura interessante, certo, servirebbe un lettore con conoscenze di informatica e matematica degli algoritmi decisamente superiore alla mia per poterlo apprezzare. D'altra parte la metabiologia sta nascendo effettivamente in questi anni, come primo abbozzo di teoria dopo che da tempo se ne parla. Ricordo accenni al tempo di alcuni miei corsi, e sono passati almeno 15 anni. Come dice l'autore nel capitolo chiave, il 5, "L'informatica teorica è biologia teorica".
Non sono d'accordo su alcune sue affermazioni lievemente detrattive della matematica genetica e di popolazione, che secondo lui mancherebbe di creatività, mentre la matematica, come la biologia, è creativa. In realtà sta parlando di uno strumento dall'uso ben specifico, e dunque non può essere creativo. La creatività sta in chi lo usa, non nello strumento in se.