The Map is not the Territory

I came across this charming historical map while following one of my favourite Twitter feeds “@Libroantiguo” which publishes fascinating material about books of all kinds, especially old ones. It shows the location of London coffee houses and is itself constructed in the shape of a coffee pot:

Coffee
Although this one is obviously just a bit of fun, maps like this are quite fascinating, not only as practical guides to navigating a transport system but also because they often stand up very well as works of art. It’s also interesting how they evolve with time  because of changes to the network and also changing ideas about stylistic matters.

A familiar example is the London Underground or Tube map. There is a fascinating website depicting the evolutionary history of this famous piece of graphic design. Early versions simply portrayed the railway lines inset into a normal geographical map which made them rather complicated, as the real layout of the lines is far from regular. A geographically accurate depiction of the modern tube network is shown here which makes the point:

tubegeo

A revolution occurred in 1933 when Harry Beck compiled the first “modern” version of the map. His great idea was to simplify the representation of the network around a single unifying feature. To this end he turned the Central Line (in red) into a straight line travelling left to right across the centre of the page, only changing direction at the extremities. All other lines were also distorted to run basically either North-South or East-West and produce a regular pattern, abandoning any attempt to represent the “real” geometry of the system but preserving its topology (i.e. its connectivity).  Here is an early version of his beautiful construction:

Note that although this a “modern” map in terms of how it represents the layout, it does look rather dated in terms of other design elements such as the border and typefaces used. We tend not to notice how much we surround the essential things, which tend to last, with embellishments that date very quickly.

More modern versions of this map that you can get at tube stations and the like rather spoil the idea by introducing a kink in the central line to accommodate the complexity of the interchange between Bank and Monument stations as well as generally buggering about with the predominantly  rectilinear arrangement of the previous design:

I quite often use this map when I’m giving popular talks about physics. I think it illustrates quite nicely some of the philosophical issues related with theoretical representations of nature. I think of theories as being like maps, i.e. as attempts to make a useful representation of some  aspects of external reality. By useful, I mean the things we can use to make tests. However, there is a persistent tendency for some scientists to confuse the theory and the reality it is supposed to describe, especially a tendency to assert there is a one-to-one relationship between all elements of reality and the corresponding elements in the theoretical picture. This confusion was stated most succintly by the Polish scientist Alfred Korzybski in his memorable aphorism :

The map is not the territory.

I see this problem written particularly large with those physicists who persistently identify the landscape of string-theoretical possibilities with a multiverse of physically existing domains in which all these are realised. Of course, the Universe might be like that but it’s by no means clear to me that it has to be. I think we just don’t know what we’re doing well enough to know as much as we like to think we do.

A theory is also surrounded by a penumbra of non-testable elements, including those concepts that we use to translate the mathematical language of physics into everday words. We shouldn’t forget that many equations of physics have survived for a long time, but their interpretation has changed radically over the years.

The inevitable gap that lies between theory and reality does not mean that physics is a useless waste of time, it just means that its scope is limited. The Tube  map is not complete or accurate in all respects, but it’s excellent for what it was made for. Physics goes down the tubes when it loses sight of its key requirement: to be testable.

In any case, an attempt to make a grand unified theory of the London Underground system would no doubt produce a monstrous thing so unwieldly that it would be useless in practice. I think there’s a lesson there for string theorists too…

Now, anyone for a game of Mornington Crescent?

 

13 Responses to “The Map is not the Territory”

  1. Adrian Burd Says:

    Elephant and Castle

  2. Max Tegmark in some sense advocates an extreme version of what could be seen as the opposite point of view. I think it’s worth checking out, even if you don’t agree with his conclusions. (In other words, to echo the title of a recent post here, if he is wrong, then on a higher level, a level to which most mortals don’t aspire, much less reach.) He has also written a popular book expounding this idea and embedding it in a general overview of cosmology and quantum mechanics. In the book, he is careful to distinguish between mainstream stuff, slightly speculative stuff, and really speculative stuff.

    • Anton Garrett Says:

      Hmm. When a leading cosmologist talks about cosmology, I listen and learn with respect. When he talks philosophy, I consider him no more or less likely to talk sense than anyone else with a decent education.

      It has been the fashion for a while for popularisers (and some scientists who should know better) to assert that physics, ie the universe, IS mathematics. I regard this as nonsense, or at the very least unprovable metaphysics. Ever since a formalism for better prediction emerged (ie, quantum theory) in which some elements of the formalism did not correspond to things “out there”, there has been confusion. But this fact might merely be because a deeper level existing “out there” has not yet been accessed by our experiments.

      Mathematics is about abstraction. You get the idea of “three” from what it is that three boats in a harbour, three coins on a table, three sheep in a field etc have in common. (This definition is not reflexive, because I could show you pictures of these scenarios rather than describe them in words.) When, in physics, I say “three volts”, “volts” is a concept OUT THERE just like the boats, coins and sheep. Of course you can go solipsist if you want and say that these things are really your sensory impressions, but then it is remarkable that other people whom you suppose to be illusions agree about the numbers.

      Tegmark’s paper is in the same category as Bishop Barnes’ Gifford lectures which in the 1930s discussed Christian theology and also threw in the field equations of general relativity. Tegmark throws in philosophy rather than theology, but in either case the connection between the two is either nonexistent or much deeper and more subtle than as expounded.

      • Who apart from Tegmark makes this claim?

        Tegmark is careful to avoid the trap of solipsism and also claims that his hypothesis is testable in the Popperian since.

      • Anton Garrett Says:

        Penrose started it. And I think Barrow, although I’ve read only summaries of what he says. But it’s “in the wind”; surely you have encountered it?

      • Barrow and Penrose have both certainly written a lot about physics and mathematics, but I don’t remember either making such a strong claim.

      • Anton Garrett Says:

        Penrose said it in relation to networks of pure numbers which at one time he suggested underlay twistors. The suggestion also appears as a summary on the back cover of one of Barrow’s books. I tried to find which on Amazon but he has written so many popular books so quickly and not all have the back cover viewable.

  3. Anton Garrett Says:

    The first map brings to mind the whimsical idea of a coffee crawl rather than a pub crawl…

    Have you come across the books of ER Tufte on visual conveyancing of information? He’s brilliant.

  4. […] hubristic notion of “post-empirical” science is the related troublesome confusion, as highlighted by Peter Coles, between the map and the territory. A mathematical model is exactly that — a model. We will […]

  5. […] realise how many maps and other designs rely on full colour perception for their effect. I’ve previously celebrated the London Underground map as an excellent example of graphic design, but it must be a nightmare to […]

  6. […] realise how many maps and other designs rely on full colour perception for their effect. I’ve previously celebrated the London Underground map as an excellent example of graphic design, but it must be a nightmare to […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: