Criticisms on Criticisms on a New Kind of Science

By Xah Lee. Date: . Last updated:

This page is a criticism on criticisms on the book A New Kind of Science.

Words Wolfram Likes to Use

Some words Wolfram likes to use in his writings: fundamental, quite, rather, “it turns out”, “kind”. Usually used in a manner to qualify his sentence so that it is still true in a broader, general context, but often just makes his statements hazy.

Here's a typical example from p170: “… adding more dimensions does not ultimately seem to have much effect on the occurrence of behavior of any significant complexity.”.

Non-Standard Terminology and Notation

The following are excerpt from: Critical Review of “A New Kind of Science” , by David Drysdale.

Part of the problem is Wolfram's insistance on using his own terminology for concepts and ideas that have perfectly good names in regular mathematics and science. Examples: he always referring to fractals as “nested” (and never makes clear whether the term includes less structured fractals or not), he doesn't refer to well-known pictures by their common name in the main text (such as the Sierpinski gasket or the Koch curve), he calls refers to lossy compression as “irreversible”, he insists on using Mathematica notation rather than standard mathematical notation (there may indeed be a million Mathematica users, but there are considerably more who understand normal notation and don't have access to this expensive tool).

There are good justification on the way Wolfram uses his own terms, at least some of them. Usually, Wolfram terms, in my opinion, are better technical terminologies, judged from the point of view on the quality of scientific terminologies. For example, “Sierpinski gasket” or the “Koch curve” conveys nothing about what they are. (one class of scientific jargons that are bad quality is those after a person's name.) Most scientific terms arose and got adopted are due to circumstantial happenings (much like natural languages such as English (For example, “cool guy”, “hot chick”, “Okay”)), not due to design or thought. Thus, a significant portion of scientific terminologies, are rather misleading or blank label, and in general contribute to confusion of the field, in particular in education and for students. (“student” here are anyone learning the field, including expert in other fields) [see Math Terminology and Naming of Things]

The term “lossy compression” vs “irreversible compression” are somewhat a tie with regards to the term's quality. They just emphasize 2 different aspects.

Wolfram's use of Mathematica notation instead of traditional math notation, in my opinion, is a good move. First of all, there are selfish motive since after all his company sells Mathematica. But, traditional math notation, as a evolutionary product like languages and terminologies, has a lot ambiguities. Mathematica's notation, is in a sense a actual formal system since it runs as a computer program. In practice, when math notation is used in the book, it doesn't matter whether traditional math notation is used or Mathematica. If the notation is about math, there's little difference other than a few Capitalization or parenthesis (For example, Sin[x] vs sin(x)). If the notation is a computing code, one has to chose a language anyway. [see The Problems of Traditional Math Notation]

Writing Style

It is true that the book is full of aggrandizing bloat. I think, the texts in the book can be made to be 3/4 of its size without losing any info, including keeping intact Wolfram's opinion of himself, and maintaining a readability at the generally intelligent. The bloat and repetition really makes the book hard to read and fuzzy. It is difficult to discern what is exactly claimed.

The justification for his writing style, given on p849., is not that convincing. It basically just further aggrandize himself more.

Particularly annoying to me is that each and every paragraphs are just 1 to 3 short sentences, the tireless repetition that simple program generates complex behavior, and insistence of his genius. This adds a lot burden to extracting the technical info in the text.

However, i do support certain aspect of the writing style being non-conformal, opposing the standard styles as seen in math journals. Here's few elements that i despise in standard style:

Abuse of Jargons

Publications done by most academicians, including textbooks, tend to use jargons unnecessarily. The reason is precisely to make the text sound more sophisticated. This in fact has become the norm, especially in academic community. Wolfram's NKOS went the other extreme by avoiding jargons entirely, and traditionally recognized lingoes are used only in the Notes section. This is a excellent exposition principle.

Academicians, as human animals, use jargons intentionally or subconsciously to aggrandize themselves. Wolfram overtly and consciously aggrandize himself, but avoid opaque jargons. (See: World Multiconference on Systemics, Cybernetics and Informatics)

Bibliography as Long List of Titles

The purpose of bibliography is for citing results of the text, or acknowledgment, or to give readers further reference. However, typical academic bibliography tends to be just a huge list of incomprehensible titles, as if to show how erudite the author is. The reader, including other researchers, often have no idea which book sections is significant or worth reading in relation what part of text.

This problem is especially important today, when there are crazy amount of publications in any field. It would be much better, if standard publication force authors to use annotated bibliography. Wolfram's General Notes section, at least do away with such inane list of titles. In fact, he takes the approach of comprehensive survey, with copious commentary. (albeit with possibly many other flaws such as aggrandizing himself or belittle forerunners.)

Useless modesty

When publishing a book, honesty of what one perceives to be important is more important than being modest. A fundamental aspect of modesty, is a social behavior to advance himself (much like politeness). So, in many publications, the author would use “We” as opposed to “I” (which is a historical, social development), even in cases where the author alone worked on it.

It would be better, if publication adopt more emphasis on truth, i.e. the raw thoughts of the author, as opposed to inducing the author to introduce elements of modesty. Perhaps Stephen Wolfram is overdoing the honesty bit, or perhaps he truely thought himself as the greatest genius. But at least, we can attack him as he is (which is exactly what happened), as opposed to having a politeness that meddles criticisms (many reviews of books in fact are hampered with politeness or the social relation of the persons involved).

Of course, modesty, politeness, are both well studied critical elements of influence and marketing. Easy way to see this is to look at politicians.

Pedantic English grammar

If you have fair amount study of writing, linguistic, logic, you'd know that there are many illogicality and intricacies of natural languages especially English. Conventional English grammar or writing style, often is not completely compatible with clarity and precision. I do find Wolfram's writing style hampers reading (all things considered), but not for breaking conventional English writing style at the grammar or syntax level, per se. For example, i think starting a sentences with words like “And”, “But”, “So” is not a problem by itself.

In relation to the above ideas, see:

The Significance of the Book

Many reviewers, in particular some mathematicians and scientists, completely dismiss the book as crank. (e.g. [A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity By Cosma Shalizi. At , accessed on 2015-12-03 ] (local copy A_Rare_Blend_of_Monster_Raving_Egomania_and_Utter_Batshit_Insanity_by_Cosma_Shalizi.txt ) ) Perhaps the falsity of these reviews are obvious, or that they really just wanted to attack Stephen Wolfram. (it is well known that Wolfram is cocky and has offended many notable mathematicians and scientists. But also, fighting and power struggle in the field of math or science is common and well documented in history) However, here i like to list some less commonly cited reasons why the book is considerable. (the commonly cited reasons include the proof of 110 CA by Matthew Cook and Wolfram's shortest axioms for logic. (p808.) )

A Survey of Simple Systems

The book exams thousands of cellular automata (CA) or other simple systems and made a report of it. (especially chapters 1 to 6) These explorations, are not trivial. From this aspect, the book can be considered significant at least as a average scientific publication at the research level.

A Recreational Math Text

The General Notes section (p849 to p1197), of 348 pages in small print, can be considered significant at the level of textbook, of a person's survey of the sciences and mathematics in relation to CA.

For example, there are lots of books published aimed at the general public, including science popularizing books, recreational math books, computer programing books, and many received great accolades and awards. (e.g. • Douglas R Hofstadter's Gödel, Escher, Bach Buy at amazon. • Martin Gardner's creational math collections. Buy at amazonWilliam Poundstone's Labyrinths of Reason Buy at amazon. • Tristan Needham's Visual Complex Analysis Buy at amazon.) These books are not scientific publications or news-breaking discovery, but nevertheless are valuable for at least education. Considering the actual info content of Wolfram's book especially the General Notes, it has value at least as significant as these books.

Exemplary Exhibition of Scientific Visualization

Edward Tufte has written books on Scientific Visualization Buy at amazon that are widely acclaimed. In my opinion, it is rather trivial to exposit on this matter, as i believe any intelligent person who has put thoughts into creating her illustrations should arrive at the same conclusions or practices. Nevertheless, Edward's book is widely acclaimed in the scientific community. Also, there are awards and seminars in the scientific community for visualization. Wikipedia goes as far to have a article on Information design with citations of journals, organizations, and books published by MIT press. So, these facts tells us that scientific visualization are highly valued by the scientific community.

Wolfram's book, in its 1k+ illustrations, are examples of the finest quality of scientific visualization. Mathematica is a powerful tool in creating illustrations, but even for a expert Mathematica programer, a significant percentage of illustrations contained in Wolfram's book are not trivial to create. Some types of the illustrations, for example, involving networks, Ant CA, 3D CA, complex graph of replacement systems with arrows, etc, will take a expert programer days to create, for each. (or months each, to actually create a robust program as seen in many Java applets on the web created by programers) Perhaps most of these are coded by Wolfram's employees, but nevertheless, the book itself is significant at least for its exemplary exhibition of highest quality and quantity of scientific visualization. If Wolfram wrote and published his ideas in a normal way, it would no doubt win awards.

As Social Movement

Entrepreneurs, even though have contributed nothing to science, but are highly valued by society. In fact, science would make little progress without entrepreneurs. This is a basic understanding for anyone acquainted with sociology. Likewise are great figures in history remembered as educators, reformers. Wolfram, due to his wealth, his success with Mathematica, and at least his recognization as a genius for his past contribution to physics, has made his book a relative major impact in the science community. He also, subsequently started a series of websites, lectures, and school for the type of research he is interested in (i.e. what he calls the New Kind of Science). Unless the study of cellular automata is completely worthless for anything whatsoever in science (which is not true), one must then give credit to Wolfram at least as a educator or science popularizer, who made the general public aware of a particular math subject, or made a movement in scientific community, or the programing community, on CA. In short, he made a significant influence.

Arguably, popularizing science is only a side effect of his book, where he actually intended to popularize himself. But nevertheless, the end result of his book and websites and investments into simple programs research, has made non-trivial contribution to science. For example, in 2007 Wolfram offered $25k US dollars for proving or disproving whether Wolfram's 2-state 3-symbol Turing machine is universal. This award is won by Alex Smith, but the proof is however disputed by a well-known computer scientist Vaughan Pratt. If the proof is correct, then this is a significant contribution to science instigated by money (For example, the Millennium Prize ). If this proof is incorrect, arguably, it contributed to science of more precise understanding of what is meant by universal turing machine.

Other Sites

Collection of books Stephen Wolfram owns:

[Notes on “A New Kind of Science” By David Drysdale. At , accessed on 2012-03-22 ] (local copy Notes_on_A_New_Kind_of_Science_by_David_Drysdale.txt)

Collection of reviews. [A Collection of Reviews of ANKOS and Links to Related Work By Edwin Clark. At , accessed on 2015-12-03 ]