## April 26, 2011

### The Colours of Infinity — A Review

#### Posted by Tom Leinster

Horribly late — sorry, Fernando! — I just sent in a review of The Colours of Infinity, a popular book on fractals. It’s for the online reviews of the Mathematical Association of America.

It’s not entirely complimentary. You could also call it unfair: I’ve judged the book by its interest to mathematicians (because that’s what I was asked to do), whereas it plainly wasn’t written for that readership. You can read my review here, and for balance you can read some much more positive reviews at Amazon.

For the first time ever, I’ve used a Creative Commons licence. I’ve been interested for a while in finding out about Creative Commons licences, and I thought I’d take the plunge by using one on something of relatively low importance. Call it jumping in at the shallow end.

Creative Commons has a range of licences, depending on factors such as whether you want to allow commercial use of your work and whether you want to allow other people to modify it. They have a handy licence chooser. For this review, I decided to use the most liberal licence: so in the unlikely event that you want to rewrite my review and sell it, you’re free to do so.

Posted at April 26, 2011 11:52 PM UTC

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### Re: The Colours of Infinity — A Review

Posted by: increpare on April 27, 2011 1:30 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Also, I MADE A CUP OF TEA.

Posted by: Tom Leinster on April 27, 2011 2:49 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Reminds me somewhat of the open access Pre-Calc textbook. Licensed under “no derivatives”…

Posted by: Peter LeFanu Lumsdaine on April 27, 2011 2:05 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Tom, did you click on the link? This is the sort of thing I meant when I said below about choosing the “no derivatives” version of the licence (and I suspect that the poster was posting it precisely to make that point). I admit that first time around, I misread it and didn’t click through due to confusing “derivative” with “derivative” - it took Peter’s comment below to clear up the confusion for me!

The thing to consider is that leading sentence “based on an article by Tom Leinster”. Most readers of the derivative work will not click through to read the original article (though in this case they will do so since the derivative is gibberish!) and see how much has been distorted or changed. Thus although legally you are disassociated from the derivative work, in the minds of the readers you will not be. Indeed, someone could go through your review and carefully negate every sentence and republish it as a “derivative work”.

Posted by: Andrew Stacey on April 28, 2011 8:59 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Yes, I take your point. It’s a good one. And yes, I clicked on that link as soon as it appeared.

One thing that got me interested in CC licences was a conversation with Sasha Borovik in which he enthused about editable textbooks and the good they do for society at large. If we’re all going to get scared about people adapting our work, that puts a damper on things.

Also, I note the following item from the FAQ at the Creative Commons website:

I don’t like the way a person has used my work in a derivative work or included it in a collective work; what can I do?

If you do not like the way that a person has made a derivative work or incorporated your work into a collective work, under the Creative Commons licenses, you may request removal of your name from the derivative work or the collective work.

I haven’t found out what’s behind “you may request”. Obviously you may request anything you like. Do they mean that the maker of the derivative work is obliged under the terms of the licence to remove your name if you so request?

Posted by: Tom Leinster on April 28, 2011 1:09 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

To answer my own question: yes, apparently they are so obliged. From the legal terms of the licence I used:

If You create an Adaptation, upon notice from any Licensor You must, to the extent practicable, remove from the Adaptation any credit as required by Section 4(b), as requested.

(Section 4(b) basically says that people making derivative works must credit the original author unless requested otherwise.)

So if I was bothered by the gobbledegook derivative that increpare made, I could request my name to be removed from it. I must admit that I was actually freaked out for a minute when I first saw it: the bizarre gibberish nature of the derivative, the capital letters in the comment, and the lack of real name made me feel that I was being stalked by a psycho. But then I calmed down.

Posted by: Tom Leinster on April 28, 2011 1:22 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Oh, I’m not a psycho stalker (though I certainly like your work :) ). I tossed it through this

http://ded.increpare.com/~locus/WordRearrange.html

a tool that I made for a composer acquaintance to save him some manual labour.

(Not being mathematically active, and the post being an off-the-cuff thing, I didn’t see much point in using my real name (which is Stephen Lavelle) ).

Apologies for any alarm caused, ‘twas intended to be immediately perceived as light-hearted.

Posted by: increpare on April 28, 2011 5:37 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

OK, thanks! No problem at all, and I hope you can understand my momentary consternation.

Posted by: Tom Leinster on April 28, 2011 5:41 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

I’m also very much in favour of the CC-type licences. But one thing I’ve learnt in the past few weeks is that there are many different ones out there and not all are suitable for everything. GPL is great for code, but not so good for documents, CCs are great for documents, but not for code. And if you want to mix-and-match stuff, then there can be competing conditions on the licences so it well behoves you to choose carefully.

For opinion pieces, then I don’t see the need to allow derivatives and can see several arguments for not allowing them, so I would choose one that allowed distribution but not modification.

For textbooks, I would definitely allow modification as one of the values of having that sort of textbook would be that lecturers could easily adapt them to the needs of the course (rather than having to adapt the course to the needs of the textbook, as so often happens). Some licences allow you to designate certain sections as “immutable”, meaning that they cannot be changed. I can envision a situation where the introduction was considered “one unit” (which could be included or not, but not modified), and the main text was modifiable.

(There are a couple of linear algebra textbooks that have been released under the GPL, by the way.)

For articles, I would want a different licence; perhaps the Mathematics Public Licence. I would want it to be something like:

1. You are free (indeed, encouraged!) to take the mathematical ideas and modify them as much as you like. This includes verbatim copying of theorems, definitions, and proofs. But you are required to refer to the original article.
2. You are free to distribute the article as a whole, providing its content is unchanged. You may modify the formatting or presentation style to suit. In particular, you may convert it to another format (for example, an accessible format). Any modified version should contain a reference to an unmodified version.
3. Any modification must be released under a likewise licence.

One could argue that mathematics is in the public domain anyway, but as the CC0 licence points out, sometimes it is good to explicitly put stuff in to the public domain. Also, licences like the GPL exist to ensure that stuff that is, to all intents and purposes, in the public domain stay there.

Posted by: Andrew Stacey on April 28, 2011 1:29 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

For opinion pieces, then I don’t see the need to allow derivatives and can see several arguments for not allowing them, so I would choose one that allowed distribution but not modification.

I agree. In an earlier comment you asked why I chose a licence that allowed derivatives of my review. It was purely experimental: up until now, I simply hadn’t thought about this issue.

Posted by: Tom Leinster on April 28, 2011 1:34 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

You are free (indeed, encouraged!) to take the mathematical ideas and modify them as much as you like.

Is that really necessary, or even possible, to specify in a license? My understanding was that ideas cannot be copyrighted.

I would also have guessed that copying of theorems and definitions verbatim, at least, would be covered under fair use, although probably not long proofs (of course, some articles are basically nothing but a long proof).

This also makes me wonder: what about formalized mathematics? It is mathematics, but it is also basically a computer program, and we should expect future mathematicians to want to modify it and incorporate it into their own proofs in the same way that programmers do. Perhaps we should regard ordinary written mathematics as analogous to the documentation of formalized mathematics? (With the amusing consequence that until very recently mathematicians have been doing nothing but writing specifications for code that didn’t exist yet.)

Posted by: Mike Shulman on April 28, 2011 7:08 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Certainly one has to distinguish between an idea and the language used to write it down. But even informal mathematics is much more formal than everyday writing and if I were to find a theorem in some paper that I wanted to use, it is highly likely that I wouldn’t want to change any part of it, and it would be inconvenient to do so (should I change all my manifolds to N instead of M?). One of the purposes (as I see it) of things like the GPL and CC are to take these grey areas where everyone understands what’s allowed, but no-one says so explicitly, and ensure that no-one can come along later and move the boundaries without us noticing.

“Fair use”, by the way, is ambiguous and country-specific. From what I remember reading, there is no such concept in British law (I could very well be mistaken).

Posted by: Andrew Stacey on April 29, 2011 12:54 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Presumably in most jurisdictions libel laws will come into play.

Posted by: Tom Ellis on April 28, 2011 3:00 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

If you feel bad about feeling compelled to write a bad review, you must check out this one in the Notices, which begins “This is a shallow book on deep matters, about which the author knows next to nothing” and becomes only more cutting from there.

Posted by: Allen Knutson on April 27, 2011 4:50 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Ah, yes, I remember that one… I think I learned about it from someone on this blog — is it possible that it was you?

I don’t really feel bad, nor would I describe it as a purely bad review. It made things much, much simpler for me that I was principally asked to assess its interest to mathematicians. Quite possibly it’s a great book for members of the general public with an interest in mathematics. And my job would have been harder if I’d had to factor in questions such as “is the pleasure gained by the general public from books of this kind more important than the distorted view of mathematics that they might promote?”

I did feel sort of vicariously embarrassed for Clarke, who was clearly an intelligent and scientifically-inclined man. There’s an appendix to his chapter showing some of his computer explorations of the Mandelbrot set, e.g. he calculates numerically the sup and inf of its intersection with the real line. I found it quite interesting to see him get excited by a piece of mathematics and try to understand it. But it’s a shame that he overextended himself so far in making all those wild pronouncements.

Posted by: Tom Leinster on April 27, 2011 5:08 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

From the review by Langlands that Allen linked to:

String theory itself or, better and more broadly, the conceptual apparatus of much of modern theoretical physics, above all of relativity theory, statistical physics and quantum field theory, whether in its original form as quantum electrodynamics, or as the basis of the standard theory of weak and strong interactions, or as string theory, is mathematics, or seems to be, although often not mathematics of a kind with which those with a traditional training are very comfortable.

Short reviews of this sentence are invited.

Posted by: Tom Leinster on April 27, 2011 5:17 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Short reviews of this sentence are invited.

Not sure what you mean by that. What is it you are after?

Posted by: Urs Schreiber on April 27, 2011 7:45 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Does Langlands mean anything more than that it has not proved easy to formulate the mathematics of modern physics with Bourbaki-like rigour?

Posted by: David Corfield on April 27, 2011 9:54 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

It’s rather long.

Posted by: Tom Ellis on April 27, 2011 10:57 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

In itself, it is an obstacle to communication - difficult to parse to say the least.

Posted by: jim stasheff on April 27, 2011 12:36 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Yes, sorry: I was just poking fun at how difficult to parse it is. It took me a good half-dozen passes to get it. Maybe I haven’t read enough German, Austen or physics. I don’t know whether it’s the German, the physics, or pure natural brilliance that allowed Urs to apparently read it without blinking.

There are similar sentences sprinkled through the review. I agree with Jim that they’re an obstacle to communication. And it’s really a stingingly negative review.

Here’s my parsing of it:

String theory itself
or
the conceptual apparatus of much of modern theoretical physics
, above all of relativity theory, statistical physics and quantum field theory
, whether in its original form as quantum electrodynamics,
or as the basis of the standard theory of weak and strong interactions,
or as string theory,
is mathematics
, or seems to be,
although often not mathematics of a kind with which those with a traditional training are very comfortable.

Posted by: Tom Leinster on April 27, 2011 3:31 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

I think Tom’s parsing gets it exactly right. If I were to rewrite that sentence, I would make a much wider use of punctuation (e.g., throw in some dashes and parentheses, to help convey the rhythm and establish dependency of clauses).

Posted by: Todd Trimble on May 4, 2011 2:35 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

I’ve seldom encountered a sentence like that written in English. It does remind me of some gems I read when taking classes on 18th and 19th century German literature (which makes Urs’s response particularly interesting to me).

Posted by: Mark Meckes on April 27, 2011 2:11 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Jane Austen is a good author to train yourself on:

If gratitude and esteem are good foundations of affection, Elizabeth’s change of sentiment will be neither improbable nor faulty. But if otherwise – if regard springing from such sources is unreasonable or unnatural, in comparison of what is so often described as arising on a first interview with its object, and even before two words have been exchanged, nothing can be said in her defence, except that she had given somewhat of a trial to the latter method in her partiality for Wickham, and that its ill success might, perhaps, authorise her to seek the other less interesting mode of attachment.

Posted by: David Corfield on April 27, 2011 2:34 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Oh dear, I was thinking this was about the content of the sentence.

How naïve of me.

Posted by: Urs Schreiber on April 27, 2011 3:56 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Henry James seemed to often write like this, at least in the later books (or so I’m told). The opening page or two of The Ambassadors give some idea of this.

Incidentally, I was once told off by an acquaintance for repeating a line I’d read in the newspaper poking fun at James’s incomprehensibility. She said that if you actually follow the sentence rather than let your eyes wander nervously over it, the meaning or description is usually clear.

Posted by: Yemon Choi on May 2, 2011 11:54 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

In defence of Langlands’s sentence, it does seem to be uniquely parseable; at least, I can’t see another solution. But I found the meaning difficult to uncover. It would be a different story if it were read out loud — I reckon that if read with the right emphasis and intonation, it could be made much more easily comprehensible.

Posted by: Tom Leinster on May 2, 2011 5:17 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

@In defense of Langlands’ sentence, it does seem to be uniquely parseable

yes, but that implies with sufficient effort

there’s at least one more such sentence in his review

I do appreciate his objection to `like you and I’, though sans context, his objection is not uniquely parseable

Posted by: jim stasheff on May 3, 2011 12:45 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Most famous for his run-on sentences is German writer and nobel laureate Thomas Mann, who used this aptly as a tool to mirror the increase of pace of events in his novel “Dr. Faustus”: As the speed of the tale increases, the length of the sentences decreases.

Maybe it was him who inspired German news agencies to impose rules that limit the length of sentences, (25 is the maximum that is desirable, 35 is the maximum that is allowed for any message forwarded to the dpa, for example).

Posted by: Tim van Beek on April 28, 2011 1:50 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

There seems to be a strong resemblance between the overselling of fractals and that of catastrophe theory in the late 60s and 70s. Arnold describes the exaggerations of the importance of the latter in his bookCatastrophe Theory. The final chapter of the book has the title The Mysticism of Catastrophe Theory.

Posted by: David Corfield on April 27, 2011 9:21 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Yes, I see what you mean.

Posted by: Tom Leinster on April 27, 2011 9:34 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

For this review, I decided to use the most liberal licence: so in the unlikely event that you want to rewrite my review and sell it, you’re free to do so.

Hate to break it to you, but that’s not the most liberal licence. The most liberal is CC0. But given that this was an opinion piece, I’m intrigued as to why you didn’t choose one of the “No Derivatives” licences. Even the FSF recommends using such a licence for opinion pieces.

Posted by: Andrew Stacey on April 27, 2011 10:45 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

As far as I can understand the legalese, though, CC0 isn’t actually a licence, or at least aims not to be under most circumstances. From its main page, for instance:

CC0 empowers yet another choice altogether […] the “no rights reserved” alternative to our licenses.

and from its FAQ:

A person using CC0 […] dedicates a work to the public domain by waiving all of his or her copyright and neighboring and related rights in a work, to the fullest extent permitted by law. If the waiver isn’t effective for any reason, then CC0 acts as a license […]

Posted by: Peter LeFanu Lumsdaine on April 27, 2011 2:10 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Standard disclaimer: I am in no way an expert on this! (But I’ve been reading these licences a little recently to ensure that we stay legal with a small spin-off project from the TeX stackexchange site http://tex.stackexchange.com.)

Technically, the CC0 is a licence. That’s because when copyright was invented, the whole idea was to take stuff out of the public domain and no-one considered that someday, someone might want to deliberately put their stuff in the public domain. So not all legal systems are set-up to cope with someone saying, “I waive everything”. Thus CC0 is a licence that has the same effect as saying “I waive everything” but says it in a legally applicable way. I have absolutely no idea whether or not Norway accepts PD declarations legally, so I don’t know if CC0 would be a licence or not in my case, but I don’t care because if a PD declaration isn’t valid here (and that would surprise me considerably) then as far as I am concerned, CC0 is as good as PD.

So the technicalities aren’t worth bothering about. Basically, CC0 “does what it says on the tin” and we don’t need to actually open the tin to check the contents. So you’re right as far as the licencee is concerned.

Posted by: Andrew Stacey on April 28, 2011 8:54 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Thanks, both. This is exactly the reason why I wanted to try out a Creative Commons licence on something I don’t care about too much, and broadcast this fact to the world: so that helpful people like you would tell me helpful things. With any luck, I’ll have learned more about the various licences and their implications by the time I come to apply one to something I care about more.

Posted by: Tom Leinster on April 27, 2011 3:09 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

We don’t seem to have a standard licence for posts here at the Café. Should we? I’m not saying that we should, I am generally ignorant of these things, it’s just a thought that has occurred to me.

Posted by: Simon Willerton on April 28, 2011 9:21 PM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

We probably should, given that it’s so easy to do. However, it’s quite likely that we’d have a 60-comment discussion of which license to pick, leaving everyone too exhausted and indecisive to actually do anything.

I have a copyright notice on every issue of This Week’s Finds and a remark that I’m reserving all rights but letting you (yes, you!) have a copy for your personal use. I haven’t bothered to stop people from reposting it in various forums. I would be annoyed if someone tried to make it into a book and sell it, but it doesn’t seem very likely since it’s free online, and full of links.

Posted by: John Baez on April 29, 2011 2:16 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

A good review! It made me want to run out and not buy the book! Here are couple of annoyingly minor stylistic comments about two sentences. The last one:

Continuing to tread this very well-worn path may not be doing any favours to mathematics, and it is a mixed blessing, at best, for those whose work involves the serious and sober study of fractal spaces.

“Serious and sober?” You sound like a dry donnish sort of fellow who sniffs at the idea of people enjoying math. There’s a New Yorker cartoon I’ve been looking for, that has two tired-out old professors sitting in overstuffed chairs in the faculty club, facing each other, with one saying:

“At least we never stooped to popularizing science.”

Since I know you’re not like that, I assume you’re going over the top deliberately, and trying to provoke a wry smile. But it’s a bit confusing, because what if I didn’t know you?

Ian Stewart is reliably excellent on applications.

I think someone must feel like they’re getting old when they’re described as “reliably” excellent. “Reliable” excellence doesn’t sound very exciting—it sounds like what you expect from a chain of hotels. I’m reminded of this remark of Gian-Carlo Rota:

The etiquette of old age does not seem to have been written up, and we have to learn it the hard way. It depends on a basic realization, which takes time to adjust to. You must realize that after reaching a certain age you are no longer viewed as a person. You become an institution, and you are treated the way institutions are treated. You are expected to behave like a piece of period furniture, an architectural landmark, or an incunabulum.

It matters little whether you keep publishing or not. If your papers are no good, they will say, “What did you expect? He is a fixture!”; and if an occasional paper of yours is found to be interesting, they will say, “What did you expect? He has been working at this all his life!” The only sensible response is to enjoy playing your newly found role as an institution.

Anyway, I hope this review of your review is perceived as the excuse for goofing around that it secretly is. Back to my drunken, giddy study of Markov chains.

Posted by: John Baez on April 29, 2011 2:42 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

A review of my review? Well, where else would I expect to find a 2-review if not the n-Category Café?

You sound like a dry donnish sort of fellow

I guess this book put me in a dry donnish sort of mood. Reading it made me thirst for some dryness. (Yes, that’s a joke.) I can only take so much of Mandelbrot banging on about how he’s revolutionized geometry, and Clarke noting the resemblance between the words Mandelbrot and mandala, before wanting to yell “for Christ’s sake, give me some intellectual rigour!”

Don’t forget that it was a review for mathematicians. If I’d been writing for the general public, it would have been entirely different.

I assume you’re going over the top deliberately, and trying to provoke a wry smile.

No, I wasn’t.

Ian Stewart is reliably excellent on applications.

That was meant positively. You say ‘“Reliable” excellence doesn’t sound very exciting’, and that’s kind of right: I wouldn’t describe that chapter as ‘very exciting’. But ‘excellent’, yes. And ‘reliably’, well, Stewart’s been doing this kind of thing for decades, and he’s usually pretty good at it. For a really long time, until the appearance of Marcus du Sautoy, he seemed to be virtually the only British mathematician willing to do this kind of public-interest work. Whenever the media needed a mathematician to interview, it was almost invariably him.

Posted by: Tom Leinster on April 29, 2011 3:48 AM | Permalink | Reply to this

### Re: The Colours of Infinity — A Review

Tom, you say:

he seemed to be virtually the only British mathematician willing to do this kind of public-interest work.

To misquote Matthew 22:

Many are willing but few are called!

The BBC and other media know they will get a good ‘performance’ from Ian and Marcus, so they call them.

Posted by: Tim Porter on April 29, 2011 8:14 AM | Permalink | Reply to this

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