04 February 2012

The Beginning Of Infinity

David Deutsch's The Beginning Of Infinity

images/boi_cover_large.jpg http://beginningofinfinity.com/

At first, I was disappointed in this book. I had liked his earlier book The Fabric Of Reality and I had high expectations. The Beginning Of Infinity seemed pedestrian after that - at first.

His main topic, the central intellectual value of good explanations, was interesting in principle, but I'd already got that from his earlier book. He describes good explanations as "hard to vary".

Then he examined themes that I was already familiar with: Evolution as unintelligent design (a la Dennett). Many-worlds. Memetics. Infinity (a la Cantor). It's hard to get excited about stuff I already knew.

Why Are Flowers Beautiful?

Chapter 14 "Why Are Flowers Beautiful?" was the first exciting offering in the book, at least to my eyes. Good art, he says is also hard to vary, just like explanation and design.

He makes his case by talking about flowers. You may think flowers peaceable creatures, but they are the product of a sort of arms race. Flowering plants are symbiotic with pollinating insects, which need to recognize them. But if their flower designs were too easy to imitate, other flowers with poorer nectar would look like them. The insects would sometimes visit the poorer flowers instead, undesirable for both the insects and the proper flowers, benefitting only the free-loading flowers.

So each flower species has an appearance that's hard to imitate. Since no flower has a monopoly on any color or shape, a free-loading flower could easily get the gross appearance right. So flowers have appearances that are "hard to vary". Getting the appearance kind of grossly right won't fool the pollinating insects.

patchworkZombie points out that this is unlikely, more likely the sincere flowers try to be memorable while free-loading flowers try to be forgettable

For flowering plants, it's a vital evolutionary design, for us, a pretty sight. This is the nexus Deutsch finds between design and art.

What does he mean, "hard to vary?"

I had to mentally fill in what he means by "hard to vary". By this point in the book I think I basically got what he meant, but he never says what he means by it in so many words. So here's my guess as to what he means by "hard to vary" as it applies to art.

What is it about art that he's saying is hard to vary? You could easily (say) play a wrong note in a Beethoven piano sonata or paint a stupid moustache on the Mona Lisa. That's not hard.

So is he saying it's hard to vary on the receiver's side? That by itself makes no sense. Of course art doesn't vary on the receiver's side, it's the artist who can make it vary, not the audience.

But if I understand rightly, it is nevertheless the audience that delineates what is "hard to vary". We can perceive some sensations and patterns easily, some with difficulty, and some not at all. Far more sophisticated than insects in many ways, but real perceptual powers and perceptual limitations nonetheless.

So an oeuvre is hard to vary if it has cornered a niche in perceptual space from which the easily-made variations produce something not much like the oeuvre. The easy variations give wrong notes and not new tunes, as it were.

It almost seems circular. Varying an oeuvre that's hard to vary produces one that is less hard to vary. That's not a good criterion for "hard to vary".

But it's really about the interaction between ease of variation and subtle perceptual powers. Varying an oeuvre in an easy way, say by changing the pitch of one note, produces something that our subtler perceptual powers see as grossly different, say, by messing up an otherwise good match to an established motif and not leading anywhere.

So if I understand right, he's saying that quality in art is precisely the same thing as being hard to vary in light of the audience's perceptual powers.

This is a good theory

It adds up to the first compelling theory of art that I have seen. It lets subjective perception into the picture, but avoids the post-modern notion that it's all subjective and "ugly is the new pretty". It's properly grounded; the concepts that it's built from are universal, not parochial, and can't be accused of being merely disguised synonyms for beauty. And most importantly, when I hold it in mind while listening to music, it seems to apply reasonably to what I'm hearing.


  1. Is he suggesting that hard-to-vary is the only property needed for beauty, or is there more to beauty than that?

  2. @John, he doesn't explicit address that, but my impression is that yes, he is saying beauty equals being hard to vary.

    He mentions other ways of being hard to vary, so it sounds like like one type of being hard to vary, qualified by subtyping conditions like being in relation to a perceiver for whom it's not directly useful, that sort of thing. But that's me filling in what he obviously just gotta, gotta mean, so take it with a grain of salt.

  3. I'm going to try to reword "hard to vary" until its meaning is obvious to me.
    "pointy peaks in the fitness landscape"? because mutations would all end up in the valleys.

    Secondly "difficult to counterfeit" flowers is not a result I would predict from an arms race between pollinators, cheating flowers and non cheating flowers.
    (I am going to talk about nectar amounts rather than pollen amounts because the plant would prefer it's pollen to not be eaten)

    In most insect-pollinated flowers, pollinators cannot detect the presence of nectar without entering the flower [paper below]. A hardworking nectar producing plant could easily mutate to not produce nectar so "hard to counterfeit" flowers are no defense against cheating flowers.
    This paper says that the observed correlation between floral display and nectar reward can be explained by the greater memorability of more impressive displays; honest plants want to be remembered cheaters want to be forgotten (and pollinators try the impressive ones first). So I do not believe that "hard to vary" is the result of the flower pollinator arms race.


    1. Nectar, that's the word I was looking for.

      I did wonder why there wouldn't be intra-species freeloading. Thank you for that. It makes sense that the selective force would be on an individaul level.

  4. Are you aware of GD Birkhoff's book Aesthetic Measure, from 1933?  (That's the father of the category-theory Birkhoff.)  I heard about it long ago from my father, who's take on it was that it was the sort of book you can't write until late in a distinguished career, so your colleagues won't dare to laugh too hard at you.  From a review in the AMS bulletin:  "Within each class of aesthetic objects, to define the order O and the complexity C so that their ratio M=O/C yields the aesthetic measure of any object in the class."

    1. I have heard of the O/C theory from somewhere (not from that book)

  5. (Okay, I'm garbling things a bit on my description of his son, who is a category-theory person in somewhat the same sense that anyone with an Erdos number of 1 is named Paul.)