On Altering Page 4 of 'A Human Document'

As I have mentioned before on this blog, I am a huge fan of Tom Phillips' A Humument, a multi-decade art project to alter the pages of an old Victorian novel, A Human Document by W.H. Mallock. The website Venus Febriculosa recently held a competition to alter a page from A Human Document, with Tom Phillips as the judge. The excellent winning entries are here, along with a few other entries, including my own, reproduced above.

On the Silence of Marcel Duchamp

Via: http://may-contain-peanuts.tumblr.com/ via the inimitable http://boingboing.net/.

On the Release of the Paperback Version of My Novel

The paperback version of my novel came out on June 10, 2015. Ask for it at your local bookstore or buy it on Amazon.com. You can read more about it here on GoodReads.com.

Or check out these review excerpts:

"Part treatise on art appreciation, part humorous on-the-road tale, neuropsychologist Westbury’s debut novel offers a compelling story about the role art can play to disrupt, delay, and contribute to human engagement with the real world. —Booklist

"Westbury’s Bride Stripped Bare contains many layers. It has, among other elements, a road trip, an unusual love triangle, cross-dressing, anagrams, off-kilter theories of religion, a handmade chocolate grinder, and a see-how-many-balls-I-can-keep-in-the-air comic structure that adds to the novel’s overall buoyancy." —Edmonton Journal

"Part treatise on art appreciation, part humorous on-the-road tale, neuropsychologist Westbury’s debut novel offers a compelling story about the role art can play to disrupt, delay, and contribute to human engagement with the real world." —Booklist

"It’s a sweet story, and it builds inevitably to a happy ending." —Kirkus

"Clever, funny, and fun, and filled with great discussions about art" —BookRiot

"Bright aesthetic discussion amid mishap; not just for the college-nostalgic but for anyone who enjoys a rush of ideas while being entertained." —Library Journal, Top Summer Reads 2014

"Westbury, a cognitive neuropsychologist at the University of Alberta (Edmonton), has plenty to say about art and attention, about the line between sanity and mental illness, and about the nature of a well-lived life... Westbury's debut is a call to pay attention, and a reminder of the rewards of patience and open eyes." —Barnes & Noble Review

On The Pleasure of Having My Book on The Leacock Medal Long List

I am very happy to see my novel is included on the long list for the 2015 Stephen Leacock Medal for Canadian humour writing! The medal is named after the well-known Canadian humour writer, pictured above.

On The Mis-cited Magic of the Number 7+/-2

 [Figure 6, reproduced from George Miller's (1956) paper  

The Magic Number 7 (+/- 2): Some limits on our capacity for processing information.  

N.B. The y-axis in this figure is in bits, not items.]

[This post has been edited since its initial posting, 

to correct some inexactitudes in the original text]

“It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”
                                                            - Josh Billings

One thing that everyone knows, perhaps one of the most widely cited facts of psychology, is that the capacity of short-term memory is 7+/-2 chunks, where a 'chunk' is some potentially complex (multidimensional) unit. Everyone knows that this fact was first discovered by George Miller, and that it was reported in a famous paper in 1956, called The Magic Number 7 (+/- 2): Some limits on our capacity for processing information, which often shows up as the first or second most cited paper in psychology. However, it seems very few people bother to read what Miller wrote. Although the fact attributed to the paper is mentioned in passing, it is not the main focus of the paper, Miller did not ever pretend to have discovered it himself, and he did not really say that we could remember just 7+/-2 things.

When I read this charmingly-written paper, I was surprised by several things.

The first surprise is a rather minor one: the paper contains no new data. It is a review paper. This surprise is really neither here nor there, since it matters little who actually collected the relevant data. There are lots of empirical data in the paper.

The second surprise is that the paper is written in information-theoretic terms. This matters because Miller moves back and forth between talking about the amount of information (Shannon entropy) a person can remember and the number of items a person can remember. That these are not the same thing is one of the main points of the paper.

The third surprise in Miller's paper is that the ‘7+/- 2’ is not always referring to number of items, but at first to a standard deviation bound. One of the main points of the paper for Miller is the fact that the number 7 (approximately) shows up all over the place. He begins by considering recognition of simple (one-dimensional) stimuli and concludes "If I take the best estimates I can get of the channel capacities for all the stimulus variables I have mentioned, the mean is 2.6 bits [= 6.3 items] and the standard deviation is only 0.6 bit [=1.5 items]." So here we see the first appearance of 7+/-2 (sort of): Miller notes that a person can usually accurately recognize 6.3 one-dimensional items (eh, that's nearly 7) with a standard deviation (not an upper and lower bound) of 1.5 (close enough to 2, for sure, if we squint). Two standard deviations includes about 95% of a normal distribution, so if we want state Miller's law properly with an (approximate) upper and lower bound (a 95% confidence interval), it should not be 7+/-2, but 6.5+/-3 [i.e. the average +/- (2 * the standard deviation)]. This is Miller's first '7'.

The fourth and biggest surprise in his paper is the big one: that Miller does not really argue that the human short term memory capacity is approximately 7 +/- 2 items. In fact, he explicitly rejects this, noting that "Everyday experience teaches us that we can identify accurately any one of several hundred faces, any one of several thousand words, any one of several thousand objects, etc. [...] We must have some understanding of why the one-dimensional variables we judge in the laboratory give results so far out of line with what we do constantly in our behavior outside the laboratory" [Emphasis added]. After he has discussed the experiments on recognition memory for one-dimensional stimuli and established the 6.5+/-3 finding, he turns his attention to discussing recognition memory for multidimensional stimuli: that is, stimuli that have more than one dimension of variability. A simple example (though just one of several considered in the paper) is the difference between how people do at recalling previously-seen points on a segmented line (one dimension) and how they do at recalling previously-seen points on a square grid (two dimensions). For points on a line, people have a memory capacity of about 3.25 bits (9 items). For points on a grid, they have a memory capacity of about 4.6 bits (24 items)! So much for a short-term memory capacity of 7+/-2 (at least for recognition memory)!

Miller goes on to estimate how far this improvement due to multi-dimensionality can be taken. Extrapolating by eye-balling ("in a moment of considerable daring", as he notes) from the available data that looked at multiple dimensions of variability [see figure reproduced above], Miller estimates that the 'real' multidimensional capacity of human short-term memory is about 7.2 bits, or 150 items, "up into the range that ordinary experience would lead us to expect". This is Miller's second '7': it is a 7 bit limit, 150 items. 

This is drawn from studies that manipulated at most six dimensions, but Miller writes "I suspect that there is [...] a span of perceptual dimensionality and that this span is somewhere in the neighborhood of ten, but I must add at once that there is no objective evidence to support this suspicion." Later in the paper he rounds this suspicion to....his third 7! He writes "I have just shown you that there is a span of absolute judgment that can distinguish about seven categories"[emphasis added], though in fact he looked at data that manipulated six categories, and guessed people might go be able to go as high as ten. Well, 6 and 10 are approximately 7+/-2 so...yeah, close enough.

The fourth 7 that Miller discusses is the so-called subitization limit, the number of things a person can enumerate at a glance. He notes that "there is a span of attention that will encompass about six objects at a glance" (well, 6 is more or less 7).

Finally, Miller discusses a fifth 7, his most famous one. At the end of the paper, is his deservedly-famous discussion of chunking, he reviews data collected by others showing that “With binary items the span is about nine […] although it drops to about five with monosyllabic English” and then shows this in Figure 7. Here Miller has switched tasks. His initial discussion was about the recognition memory task called absolute judgment (the experimenter presents N unnamed but coded [usually numbered] stimuli, then presents one of them again and asks the participant which one it was), on which his point is, as noted above, that people can do very well far beyond 7+/2 items. The final discussion is about ordered memory span: the experimenter presents N named stimuli (words, numbers, letters) and asks the subject to repeat all of them back in order. If by ‘memory span’ you mean ‘number of things a person can hold in short term memory’, then Miller’s review of multidimensional absolute judgment experiments shows that it is far above 7+/-2, as common sense suggests it must be. If you mean ‘number of items you can repeat back in order without error’ then Miller’s paper reviews data suggesting it is 5 to 9 items, the magical 7+/-2. As others have noted, the ordering requirement is itself adding to the magnitude of the memory problem, because the stimulus order is information that has to be memorized along with the items.

The title of his paper The Magic Number 7 (+/- 2) was selected not because that is the span of short-term memory (which it is not), but rather because of Miller's remarking on the approximate equality (if we squint) of the several limits in this range that he discusses: "span of immediate memory [for one dimension of variability, 6.5 items] [...], a span of absolute judgment that can distinguish about seven categories, and [...] a span of attention that will encompass about six objects at a glance." The main point of his paper is actually that these three approximately equal limits of approximately 7 do not in fact reflect a common process, but we need not concern ourselves with that point here.

So, according to the data Miller reviews, the limit of human short term recognition memory (from his daring extrapolation) is about 7.2 bits or 150 multi-dimensional items. Moreover, he is also at pains to point out in his paper (in keeping with his observation from everyday life cited above) that this limit can be (and often is) extended by recoding and temporal chaining...

Given his own remark that everyone knows that we can easily recognize dozens or hundreds of things, it is amazing that people continue to cite Miller as 'having proved' the obviously-untrue claim that the limit of human short term memory is 7+/2 items. It really depends on how you define memory capacity.

You can read the whole paper here.

On Writing Like Designing A Ski Hill

Writing a book is like designing a ski hill. When the people you made it for are racing along, they don't even notice that they are being guided through potentially treacherous territory by careful design. They just feel free.

[Image adapted from Figure 16 of John Ruskin's (1856) Modern Painters: Volume 4.]

On Glorifying the Achievement of Winning for Love

Boingboing.net pointed out that North Korea had released a slew of new patriotic slogans, many of which seemed like something my nonsense-generating program JanusNode might have written. I used JanusNode to statistically mix together (by Markov chaining) Jenny Holzer's aphorisms and the new North Korean slogans (with a few other texts occasionally thrown into the mix) to auto-generate some new patriotic slogans. [Nonsense-generation purists: Note that as well as selecting these texts from a much larger pool, a few small human edits were made, including adding many of the exclamation marks.] See also my previous post on automating Jenny Holzer. Enjoy.

Builders! Let us glorify the achievement of winning for love!
Government is a burden on the idiosyncratic institutions!
Giving free rein to your emotions is an irresistible challenge!
Get rid of studying the enemy!
Sometimes you do crazy things for military hardware!
Moral integrity to volunteer is reactionary torture!
Manual labor can be refreshing method of our everyday life on a high level!
The Party's policies rest on the proclivity of the people to wake up wishing things are never messy!
Selflessness is the lifeline of south Korean warmongers!
Fight death-defyingly for our dear children by increased production!
Let us give full play to death, and technology!
Get rid of abuse of authority and revolution and gunners!
Get rid of abuse of authority and self-centeredness!
Symbols are parasites!
Fear is the best planning!
Love is terror-induced immobilization!
Let us raise a strong wind of stereotypes!
Let us hold fast to the props!
If you have freedom of choice, repetition is a weapon!
Electricity is the triumph of socialist patriotism!
Enrich the life of service personnel and people with credit!
Fight death!
Separatism is the same as admitting defeat!
Stupid people deserve special control!
You can't behave if they think they are important!
Random mating is good to give up if you have ugly consequences!
Knowledge should be as easy as falling off a log!
The Party's revolutions are pointless if no one notices your oldest fears!

On Having Your Shit Fucked Up

On The Egg As The Sun's Light Refracted Into Life

A fine bit of writing on the humble egg, from the excellent book On Food and Cooking: The Science and Lore of the Kitchen by Harold McGee:

"...modern science has only deepened the egg's aptness as an emblem of creation. The yolk is a stockpile of fuel obtained by the hen from seeds and leaves, which are in turn stockpiles of the sun's radiant energy. The yellow pigments [of the yolk] also come directly from plants, where they protect the chemical machinery of photosynthesis from being overwhelmed by the sun. So the egg does embody the chain of creation, from the development of the chick back through the hen to the plants that fed her, and then to the ultimate source of life's fire, the yellow sphere of the sky. An egg is the sun's light refracted into life." (p. 69; Emphasis added)

[Image: Altered detail from Plate 1 + scanning-artifact hands from John Ellard Gore (1893) The Visible Universe: Chapters on the Origin and Construction of the Heavens]

On Counting Wisps

My most popular blog post is On The Processing Speed Of The Human Brain. This post is a follow-up, asking a related question: What is the storage capacity of the human brain?

This is a difficult question to answer, because we don't really know what memories are, or how exactly the brain is storing them. It seems implausible that it is storing them in some sort of countable form, an organized set of tiles that can be plucked from the mind when needed. If you believe that the objects of the mind are less like tiles and more like the sensible wisps of a seething dynamic process, then a question about the storage capacity of the brain doesn't make  obvious sense. What exactly are we to count? All the wisping that has been sensed? All the wisping that could theoretically be sensed? The wisping that will actually be sensed by a particular person's brain? The average Shannon information of the dynamic wisping process across some specific time unit?

Some people have estimated that the storage capacity of the human brain is functionally infinite since we always find room to store more information if we want to, so no practical limit exists. This is a weak argument, since by the same argument your computer's hard disk has functionally infinite space. Perhaps the storage of the brain is constant despite our ability to always fit more in if we really have to, because we fit it in by over-writing what is already there.

A more principled lower estimate can be made by considering the hardware of the brain. A human being has about 100 billion brain cells. Let's assume that a change in any connection strength between two connected neurons is equal to one bit of information and further assume (a huge over-simplification) that neural connections have just two possible strengths (like a bit in a computer, which is either 1 or 0). Assume as we did before that each neuron connects to 1000 other neurons. Then each neuron has ‘write’ access to 1000 bits of information, or about 1 kilobyte. So we have 100 billion (number of neurons) X 1 K of storage capacity, or 100 billion kilobytes. That’s about 8 x 10^14 bits or 100 terabytes. Let's round it up to 10^15 bits, or 125 terabytes. Since in fact neural connections are not two-state but multi-state and since neuron bodies can also change their properties and thereby store information, this may be a very low estimate. On the other hand, since it counts every potential distinction as an encoded distinction (assuming no noise, no redundancy, no unused connections), it could be a huge over-estimate.

The number of bits in the brain is not equal to the number of items. For example, to store one letter of text (one item) on a computer takes a theoretical minimum of seven bits, and in real computers it usually takes more. To store one picture can take thousands or even millions of bits. The same must apply to the human brain, so if we want to count 'things' (potential wisping!) rather than bits, we need to make some adjustments for the fact that each memory must be composed of many bits.

The first person to try to estimate the amount of storage in a human brain was Robert Hooke, in 1666. He estimated how fast he could think, multiplied by his lifespan, and decided that he had 2 x 10^9 bits of storage. He had a high estimate of himself: his estimate for an average person was twenty times less, at 10^8 bits! The psychologist Tom Landauer wrote a paper in 1986 ("How Much Do People Remember? Some Estimates of the Quantity of Learned Information in Long-term Memory", Cognitive Science, volume 10, pages 477-493), in which he tried to estimate from a review of experimental results how many useful distinctions a person might be able to remember in all. His estimate was one billion relevant distinctions (10^9 bits). At a 2002 Psychonomics conference presentation that I saw, Landauer re-visited this question. He used a novel technical method (whose details need not concern us here, which is good because I can't remember them now) to estimate how much word knowledge a person had. His new estimate is in the same ball park as Hooke's: 4 x 10^8 bits. This seems implausibly low to me: that's only about 50 megabytes. I can't believe that my brain wisps as lightly as that.

Eh. I don't really think the question of how much information the brain stores has a universally compelling answer, except with some really wide error margin. Let's say: the brain can store somewhere between 10^9 bits (125 megabytes) and 10^15 bits (125 terabytes). Only [!] six orders of magnitude difference, which is good enough when we are trying to count something as abstract as a random person's potential to sense wisps.

[Image: Altered Figure 27 "The commissural connecting the cerebellum to the olivary bodies" from Thomas Laycock's (1860) Mind and Brain: Or, the Correlations of Consciousness and Organisation; with Their Applications to Philosophy, Zoology, Physiology, Mental Pathology, and the Practice of Medicine, Volume 2 ]

On Icons of the Psyche

Google released a bunch of icons for free as part of their Material Design project. I amused myself recently by considering how we might use some of them to symbolize different kinds of common thinking patterns. These are what I came up with:

            Missing the point:

            Circular thinking:

             Dwelling in the past:

            Over-focusing:

 
            Thinking outside the box:

 
            Uncertainty:

 
            Skepticism:

            Wanting a hug:

 
            Over-complication:

            Self-contradiction:

            Narcissism:

            Negative thinking:

            Defensiveness:

            Drunk:

            Suicidal:

            Need donuts urgently: 

On Painting A Vermeer

Although the story definitely moves a little slowly for a film, I very much enjoyed this documentary on how Vermeer might have used technology to paint, as much because I admire Tim Jenison's obsessive devotion to detail as because I admire Vermeer. Bravo, sir!

On Assessing the Reality of Abstract Entities

Immanuel Kant famously wrote in his (1783) Prolegomena To Any Future Metaphysics that the British skeptic philosopher David Hume had "interrupted my dogmatic slumber". As I have noted elsewhere in this blog, reading Hume myself made me realize that I was not alone in my natural inclination (since early childhood) towards doubting all things.

However, the true awakening from my dogmatic slumbers (insofar as I am yet awakened from those slumbers) occurred when I took a graduate course at McGill University in psychometrics, the mathematics of psychological measurement. My mind was blown by the idea that we could use well-motivated quantitative reasoning to assess the degree of reality of abstract entities. I am still amazed by these ideas. Now I have the privilege of teaching them at the University of Alberta.

Over the years, I have gathered a large set of quotes that try to convey to my students why I so love this idea that we can assess realism using math. I have collected a few of them below.

------------------------------------------------------------------------

    "In a word, if there is a God, all is well; and if chance rules, do not thou also be governed by it."
                            Marcus Aurelius
                            120-180 CE

---------

    "Nothing that you will learn in the course of your studies will be of the slightest possible use to you in after life — save only this — that if you work hard and intelligently, you should be able to detect when a man is talking rot, and that, in my view, is the main, if not the sole, purpose of education."
            J.A. Smith (Oxford philosopher, 1863 - 1939)

---------

    "All the real knowledge which we possess depends on methods by which we distinguish the similar from the dissimilar. The greater the number of natural distinctions this method comprehends the clearer becomes our idea of things. The more numerous the objects which employ our attention the more difficult it becomes to form such a method, and the more necessary."
                   Carolus Linnaeus / Genera Plantarum

---------

    "If we saw as much of the world as we do not see, we should be aware, in all probability, of a perpetual multiplication and variation of forms."
                        Michel de Montaigne / Essais
                        [This was the epigraph to my PhD thesis.]

---------

    "Living, just existing, presses probability to the threshold of unlikeliness."
                  Richard Powers- The Goldbug Variations

---------

    "...is not an event in fact more significant and noteworthy the greater the number of fortuities necessary to bring it about?
    Chance and chance alone has a message for us. Everything that occurs out of necessity, everything expected, repeated day in and day out, is mute. Only chance can speak to us. We read its message much as gypsies read the images made by coffee grounds at the bottom of a cup."
                        Milan Kundera / The Unbearable Lightness of Being

---------

    "...chance alone is the source of every innovation, of all creation in the biosphere. Pure chance, absolutely free but blind, at the very root of the stupendous edifice of evolution: this central concept of modern biology is no longer one among other possible or even conceivable hypotheses. It is today the sole conceivable hypothesis, the only one compatible with observed and tested fact. And nothing warrants the supposition (or the hope) that conceptions about this should, or ever could, be revised."
                        Jacques Monod / Chance & Necessity

---------

     "...algorithms of the heart, or, as they say, of the unconscious, are...coded and organized in a manner totally different from the algorithms of language. And since a great deal of conscious thought is structured in terms of the logics of language, the algorithms of the unconscious are doubly inaccessible. It is not only that the conscious mind has poor access to this material, but also the fact that when such access is achieved, e.g., in dreams, art, poetry, religion, intoxication, and the like, there is still the formidable problem of translation."
                        Gregory Bateson / Steps to an Ecology of Mind

---------

    "If there is no meaning in it, it saves a world of trouble, you know, as we needn't try to find any."
                        Lewis Carroll / Alice In Wonderland

---------

   "It's difficult to think well about 'certainty', 'probability, 'perception' , etc, But it is, if possible, still more difficult to think, or try to think, really honestly about your life & other peoples lives."
                        Ludwig Wittgenstein, in a letter to Norman Malcolm

---------

    "Research in physics has shown beyond the shadow of a doubt that in the overwhelming majority of phenomena whose regularity and invariability have led to the formulation of the postulate of causality, the common element underlying the consistency observed is chance."
                        Erwin Schrodinger / What is Natural Law?

---------

    "The most important questions of life are indeed, for the most part, really only problems of probability."
                        Pierre Simon Laplace 
                        Théorie Analytique des Probabilités (1812)

---------

    "Words are ordinarily and uncritically assumed to correspond to 'real entities' but more often than not they signify merely 'fictitious' or 'fabulous entities' having no correspondence to the substances of nature."
                        Gordon W. Allport & Henry S. Odbert (1934)/ Trait Names: A psycho-lexical study.

---------

    "It is perfectly true that we can never attain a knowledge of things as they are. We can only know their human aspect."
                        Charles S. Peirce
                        Letter to Lady Welby
                        May 20, 1911

[Image: Stylized portrait of Paul Meehl, the founder of modern psychometrics.]

On Being As Beautiful As An Encounter Between An Umbrella & A Sewing-Machine

Isidore Ducasse (1846–70) was a Uruguayan/French writer (who wrote under the pseudonym Comte de Lautréamont) who died of unknown causes at the age of 24, during the siege of Paris by Napoleon III. The Comte de Lautréamont left behind one major literary work entitled Les Chants de Maldoror, the first canto (of six) of which was self-published in 1868. The strange, dark, and incoherent work [partially readable in English translation here and fully readable in the original French here] has been described by the British novelist Richard Milward as being “like an old, twisted rulebook on how to break all literary rules”. Many years after it was published, it was discovered by the Surrealists and ardently adopted by them as a forerunner of the movement. The list of artists who produced works based on the book or its author reads like a ‘Who’s Who’ of Surrealism, including André Breton, Salvador Dalí, Max Ernst,  René Magritte, André Masson, Joan Miró, and Yves Tanguy. 

The book famously includes a description of a boy as being “as beautiful as the random encounter between an umbrella and a sewing-machine upon a dissecting-table”, a line that was cited by André Breton and Max Ernst as an example of the chance juxtaposition that the Surrealists loved. The same line inspired this (1920) Surrealist portrait of the Comte de Lautréamont by Man Ray, entitled L’Énigme d’Isidore Ducasse, now at the Tate Museum in London.

[Image from http://rigaut.blogspot.ca/2008_05_01_archive.html]

On Not Believing In What You Think You Can See

I stumbled across this 'unassumed road' in Niagara-on-the-lake, Ontario:

 

Never assume that a thing is real just because you think you can see it.