Dretske's definition of knowledge: and atoms

Dretske (Knowledge and the flow of information, CLSI 1999) page 86

K knows that s is F = K's belief that s is F is caused (or causally sustained) by the information that s is F.

Dretske argues that this is a better definition of knowledge than the 'traditional'

Knowledge is justified true belief

You have to take Dretske's definition together with his definition of information.

Consider the atomic theory of matter. Now, in what follows, you have to accept all sorts of 'suspension of skepticism', and it really needs reams of footnotes and caveats, but I think it does provide a valuable insight.

Did Democritus know that matter is structured into atoms?

Democritus did NOT know, on either definition. Although the belief was true, it was not justified because he didn't have any (modern, scientific) evidence. Similarly, Democritus's belief was not caused by the information that matter is structured into atoms

Did Rutherford know that matter is structured into atoms?

Yes, on both definitions. The belief was true, and it was justified by the experimental evidence - which was the information from his experiment.

Did a student of Democritus know that matter is structured into atoms

This I think is the key one, because I think on the 'justified true belief' a student of Democritus did know. That is, if we are going to allow anyone to learn anything 'second hand', from a teacher, then we must allow the possibility that a student of Democtritus is justified in believing his teacher. But, he does not know anything of the sort in Dretske's definition, because he did not receive the information that matter is structured into atoms.

Do I know that matter is structured into atoms?

Well, yes, I think I do know that, on both definitions. Except, of course, that there's a bit of the skeptic in me (especially, dogmatic scientific statement), but I did say above that there were all sorts of caveats and footnotes needed, and Dretske does discuss the position of the skeptic

Magna Carta

What is the significance of the Magna Carta, and where does it (the significance) come from? And especially the famous clauses (still valid today, though thought by some to be under threat in the name of national security):

(39) No free man shall be seized or imprisoned, or stripped of his rights or possessions, or outlawed or exiled, or deprived of his standing in any other way, nor will we proceed with force against him, or send others to do so, except by the lawful judgement of his equals or by the law of the land.
(40) To no one will we sell, to no one deny or delay right or justice.

72 words, 361 bytes (zips to 330), and more than* 800 years of context.
* because the context that led up to the granting of it in 1215 is as much part of its context as what happened since then.

(The full document, from the translation on the British Library site, is 4,537 words = 25,078 bytes, zips to 9,229 bytes.)

The ozone hole - information and data

In the New Scientist, an article about how NASA failed to spot the ozone hole.

The story has lots of strands, but picking out one element:

According to Pawan Bhartia, who was processing the satellite data [what the computer software collecting the data] did was "flag it up" - identifying it as unreliable. The computer, he told New Scientist, then substituted "fill values" that it thought more likely. The effect was [...] the "unreliable" data was buried and the researchers had no reason to think anything was amiss.

One of the standard things my children have been taught at school - one the things they'll get marks in the course-work for - is recognising spurious data points in graphs that you should disregard. Usually that's right, of course ("of course"? or "I suppose"?), but also risks throwing out the most important data - the data that actually gives the most information. Someone once told me that among the data that Millikan found, and disregarded, in his wonderful oil-drop experiment were some measurements that returned a value of 1/3 that of the charge of an electron - ie the charge of a quark! I don't think anyone seriously believes he'd isolated a quark (my understanding is that it isn't possible), but wouldn't that have been nice!

Dretske, and Schrödinger's cat

Dretske p69

It is silly, of course, to think of s's probably being B as itself a condition of s that we could receive information about, as something that could have a conditional probability of 1 and that therefore qualify as the informational content of a signal.

But maybe it would not be silly if s were a quantum mechanical system. We could receive the information that Schrödinger's cat is probably dead, and that could indeed be something that could have a conditional probability of 1?

("The King is probably dead: long live the King!" Where was that from? I've feeling it was in Blackadder, or did I imagine it?)

Gregory Bateson

'Everything is connected': an article about Gregory Bateson in Saturday's Guardian.

The article about Gregory Bateson (1904-80) - who famously defined information as 'a difference that makes a difference' - says things that capture something I've been increasingly conscious of.

[Gregory Bateson] reflected on the advantages of a novelist's eye when it came to describing a foreign culture: "The artist . . . can leave a great many of the most fundamental aspects of culture to be picked up not from his actual words, but from his emphasis." He can "group and stress" words "so that the reader almost unconsciously receives information which is not explicit in the sentences and which the artist would find it hard - almost impossible - to express in analytic terms. This impressionistic technique is utterly foreign to the methods of science." [...]

Dreams, religious experience, art, love - these were the phenomena that still had power.

Intentionality: landscape art, and more on Damien Hirst

I caught Channel 4's programme about landscape art in a series on sculpture last night.

Led me on a train of thought...

Waldemar Januszczak, feeling the stones at Stongehenge, talking about the 'presence' of big sculpture... Angel of the North etc... I know what he means... set me thinking: "is this not about information then?" But he then went to Nancy Holt's Sun Tunnels in the Utah desert. These are aligned with rising setting sun at the summer and winter solstices, and also have holes in them that make the sun project patterns of the stars. These facts - the solstices and the stars - only have meaning because of the information. Or rather the intention of doing this.

... why are the stones at Stonehenge art but not stones left around by glaciers?

It is the intentional information. Same reason that painting of a tree is art but the tree itself is not art.

What about the nest of a Bowerbird? Or the song of Blackbird? (Which I happen to find most beautiful.)

A related question - is the nest of a Blackbird engineering?

And on to Damien Hirst. In the Guardian on Saturday, Robert Hughes explains his objection to Damien Hirst. "One might as well get excited about seeing a halibut on a slab in Harrods food hall" he says. Perhaps it is intentionality again - the halibut in Harrods is not put there with artistic intent. Hirst's sharks in formalin were.

Dretske's definition of informational content

The first time I had a go at Dretske (Knowledge and the flow of information, Blackwell 1981, CLSI publications 1991), some years back, I remember struggling with this. I'd hit it again, on re-reading Dretske, and after some grappling with it (I just couldn't parse the sentences), think I do now get it. Here it is:

Informational Content:A signal r carries the information that s is F = The conditional probability of s's being F, given r (and k), is 1 (but, given k alone, less than 1)

This is what I think he is saying.

The equals sign is saying that what comes on the right is the definition for what is on the left. That is, what is on the right is the condition under which we can say that a signal r carries the information that s is F.

This condition is a follows.

P(s=F|r and k) = 1
and
P(s=F|k and (r not received)) < 1

Painters painting themselves

On the Today Programme

An art historian says he has found that painters who made their money specialising in portraits of famous people chose to redress the balance of power by reproducing their own facial characteristics within those of their powerful sitters. The artist Simon Abrahams explains why he calls the practice 'face fusion', and says it is evident as early as the 1600s in the work of Nicholas Hilliard and Isaac Oliver.

That doesn't surprise me at all. Everything we do, even the smallest bit of writing or drawing, contains our personality. The speaker said that art historians have made the mistake of thinking that a painting is like a photograph, when really it is like a mirror reflecting the artist's mind. I can't really believe many art historians have made that mistake, surely it has always been known that a painting is packed full of the artist. Mind you, I'm not convinced a photograph is 'just a photograph' either! The photogapher has always made choices which will be reflected in the image. I wonder, if we were to take some of our holiday snaps out of the draw at random, would someone who knows us be able to tell which were taken by me and which by my wife?

Information, causation and energy

In a comment on an earlier post, Robin Faichney said

Personally, in the most general terms, I see causation, information flow and energy flow as three different aspects of one phenomenon.

I think the relationship between the three (and matter, though that's the same thing as energy by E = mc²) warrants a lot more thought. I'm uneasy with Dretske's separation of causality and information. Shannon's equation:

C = B log(1+S/N)

links energy to information flow, since C is information capacity and S is signal energy (B is bandwidth and N noise power). However, C here is average information flow, and Dretske makes the point that engineers are always concerned with averages, whereas he is also addressing specifics. In a specific case, information can be communicated without any energy flow. "If I don't call I'll meet you at the station". The absence of a call communicates the fact that I'll meet you at the station - and causes you to go to the station to meet me.

In The Independent today...

Identifying criminals, the work of illustrators, and more on Damien Hirst.

Police identify criminals from texts.

Language scientists believe that it is possible to identify the author of a message by analysing the spelling, grammar and syntax of the words used.

My first thought was that texts are usually quite short and there is a common style of texting with many conventions, so would everyone be different - would there be enough information contained in the texts to identify people uniquely. But I can believe it, it sometime amazes me how individual people are. It would be interesting to do some quick sums on it.

Who do you think they are: Public figures put their personalities on paper.

The thread that runs through this line of picture-making is a "literary" orientation. There's some link to text or story, actual or notional.

(I've put any comments together on this yet, but want to flag it.)

There's only one way to find out what art is 'worth' – and Damien Hirst knows it.

Art has to exist within a marketplace, and Hirst is not only brave but honest in exposing the value of his art to what the market thinks of it

The marketplace, in this sense, exists entirely as information, so I think there's something useful here in the connections between the information of conceptual art and the information of the marketplace.

More on the forgery

I said

Actually, I'm not quite sure where this argument is going. I'd had in mind that I would be able to say something along the lines of Hirst's painting containing so much less information, and that therefore the value of Hirst's is almost entirely in the context, whereas Degas's contained lots of information within the painting. I'm not sure that is coming out quite so clearly.

I think the point is that it depends on how important the exact colours of each of the spots is. If the exact colour really matters, then the difference in the number of bits required for the Degas and the Hirst is not so great (assuming, of course, that the precise colour of every touch of Degas's paint brush is not equally important). If, on the other hand, it is sufficient that the dots are a range of colours, then my program which generates random colours is fine, and, with a little tweaking and zipping, I got it down to 381 bytes. I'm sure it could be reduced much further, but that's not the point, I'm interested in 'orders of magnitude' here (though I'm tempted to do something in Mathematica for the fun of it). Or I could just say "Paint circles in a 13 by 11 array, each circle x mm diameter and spaced by y mm in each direction and each circle a different colour". That's 133 characters (including spaces), so needs a 133 bytes. There's lots more to consider about the context here. Like that you already know what the words 'circle' and 'paint' mean. Anyway, my argument is that you could not describe the Degas in the same way.
Of course, there must be more to the Hirst - the type of paint, the paint surface, the brush strokes. I need someone to explain the Hirst to me. To tell me its story.

Probability of the end of the world

From The Independent on Saturday (in the print edition, I can't find it online):

The Large Hadron Collider...the possibility that it could create an apocalyptic black hole... . One estimate has put the chance at 1 in 1,019. To put that in context, you have a one in 1,011 chance of spontaneously evaporating, while you shave.

I trust that is wrong about the probability of the end of the world, and, as to the spontaneous evaporation, with millions of people shaving each morning thousands of them must be disappearing each day. I've never seen that reported in The Independent!
I presume the numbers should have been 10¹⁹ and 10¹¹, and the superscipt formatting has got lost - a common enough event. But, clearly someone has at a later stage put it the commas for the thousands, unaware of the meaning or significance of the numbers.

Forging a Damien Hirst

How much information is there in one of Damien Hirst's spot painting?

I was prompted to think again about Damien Hirst by the news of his plan to auction some of his artwork directly, bypassing the dealers.

Consider one of his spot paintings: Lysergic Acid Diethylamide (LSD). There's been a lot said about these paintings, but I want to think about their information content.

It is easy to generate an image of this painting, or something similar, on the computer. I've been playing with this.

1) Drawing an image in Adobe Illustrator. I had a go at this, aiming to match (approximately) the relative dimensions (ratio between spot diameters and spot spacing) and getting a rough match of the colours. I saved it as a jpeg file using the settings for maximum quality, which gave a file size of 110 kbytes. I've pasted it below.



At minimum quality, the files size is only 14 kbytes, but the quality is significantly reduced:



2) I then wrote a VBA macro to generate a similar image in microsoft powerpoint (I'm just using tools that I have ready to hand). Here is the complete macro to generate a diagram with the same dimensions, but randomly colouring the circles:

Sub draw_lots_spots()
col_start_pos = 25
row_start_pos = 25
For rownum = 0 To 10
For colnum = 0 To 12
col_pos = col_start_pos + colnum * 45
row_pos = row_start_pos + rownum * 45
red = Int(256 * Rnd)
green = Int(256 * Rnd)
blue = Int(256 * Rnd)
ActiveWindow.Selection.SlideRange.Shapes.AddShape(msoShapeOval, col_pos, row_pos, 24, 24).Select
With ActiveWindow.Selection.ShapeRange
.Fill.Visible = msoTrue
.Fill.Solid
.Fill.ForeColor.RGB = RGB(red, green, blue)
.Fill.Transparency = 0#
.Line.Visible = msoFalse
End With
ActiveWindow.Selection.Copy
Next colnum
Next rownum
End Sub

Saved as a text file, it is 598 bytes. (Paste this text into a VBA module in PowerPoint, then run the "draw_lots_spots" macro from a blank slide and you'll get the spots.)

3) Finally, I wrote a similar macro but combined it with a data file that contained the RGB parameters for the colours of each circle. The macro text file in this case was 636 bytes, while the data file with the colour information was 1676 bytes. Combining the macro and its data in a zip file, gave a total compressed file size of 1344 bytes.

So, what does all this say? There is a sense in which I've got an image of Hirst's LSD painting down to 1344 bytes (on the grounds that the choice of colours must have been significant). This is 'algorithmic information', and it's not many bytes - a lot fewer than required for 1919 for example. Of course, I am aware that this little image on the computer is a long way from the real meter-square painting. I'm imagining using this, from the computer, as a recipe for doing a real painting. So you could add to the VBA macro the instruction "Copy this enlarged to 106.5 cm x 127 cm using gloss paint on canvas" (or whatever was used), then you have an algorithm for getting something like the original. I don't know enough about the technique to know how close this would get you to the original. I suspect those who know might deride my suggestion that it gets you anywhere near, but it would surely get you some way towards it.

Compare this to Degas's The Bellelli Family that I discussed earlier. I can't think of any way that an algorithm could be used to construct anything resembling the painting. Compressing using JPEG, I reckon that about the minumum file size that gives you anything remotely useful is about 14 kbytes, which gives the following (I'm assuming no-one is going to worry about copyright issues with a copy - which is from the Independent article - of this poor quality)



Actually, I'm not quite sure where this argument is going. I'd had in mind that I would be able to say something along the lines of Hirst's painting containing so much less information, and that therefore the value of Hirst's is almost entirely in the context, whereas Degas's contained lots of information within the painting. I'm not sure that is coming out quite so clearly.

Enough for now. [More on this in a later post.]

Communication by art

From Gombrich The story of art

... the pre-Columbian Americans were perfectly capable of representing the human face in a lifelike manner. [...] If most works of these civilizations look remote and unnatural to us, the reason lies in the ideas they were meant to convey.

Art conveys ideas (information?) but we don't get them because we don't have the context.

We know very little about these mysterious origins, but if we want to understand the story of art we do well to remember, once in a while, that pictures and letters are really blood-relatives.