The world is conical
While reading the World is Flat I quickly became annoyed in the first chapter about the fundamental premise that the world is flat. I understood the basic idea that the world had evolved in terms of geographic barriers coming down but for me the picture of a flat world looks just like it should before Columbus. At the time geographically things were lined-up on maps so that distances can't be traversed in circles.

A number of geometric rules have been put forth to figure out what geometry that you are in that you can learn about in Feyman's Six Not So Easy Pieces in a chapter on Curved Spaceused to figure out whether Space-Time is curved or not. They generally focus on how a bug experiences their space not knowing it's contour. For example, if a bug tries to walk in a square by turning at right angles on a globe with equidistant measures they won't return to the point where they started.

Now we not only can traverse distances through low cost light speed communications/software, but to me that isn't a flat surface at all. The surface is just redefined where distance is related to the level of sophistication of the communications network and infrastructure. So flat is actually a bad way to describe how things are now. For instance I am closer to Bangalore than to Otis, MA on a telecommunications sophistication map because Bangalore is super wired while Otis hasn't gotten too far in wiring itself.

So if the world isn't flat - then what shape would it look like if we could visualize it. Some smart people at Princeton managed to visualize what the United States looks like through the lens of Presidential politics in the Princeton 2004 Election maps. So why not build some other maps about the world.

While trying to figure out the shape of the cyber-world is a wierd question it may not be possible to do and to create a new map structure from it. My first guess was that I could see the world first in a flat structure but upon adding that Bangalor is close to Boston the map would need to somehow put these points closer to each other. A reasonable way to do this would be to first flatten the map into a circle (since it is the base of a cone) with oceans towards the edges as best as possible. Then above the map build a cone ending at a point above it at the top. Rather than having mountains above the map the height of the area would rise upwards through the cone to the top based on how connected it was to the Internet, etc. If the resolution was infinite then two people talking on a telephone in cyberspace to each other would both be stretched to the top of the cone and facing each other. But since this would be an approximate map, just like the flat maps of the world not showing relief, the average in a region of connectedness to the world through a number would set the height of the peak for a region and the pull into the central point of the cone. The distance between any two places would actually no longer be readable on the lower circular map of the world but from their relative heights or a path that factored both geographic distance and the relative heights.

This new cyberworld map unfortunately would be very hard to read because things get pretty dense towards the top of a cone. If 750 cities all ended-up in a point it would have a lot of labels sticking out of it. This isn't a new problem. You can't read road signs on a map of the whole globe. You need to be able to zoom in and out. So one solution is to be able to change the view from the bottom to the top. At the bottom you have standard road sign problems but since the top condenses a lot your views probably should take cross sections - from height a-b and display what's in them labelled correctly.

In another way to approach this the world could be looked at with two dimensions. Each point would be defined A) by a two dimensional E-W land area (like a district, suburb, etc.) and B) by a number from zero to one representing a measurment number. The reason for measuring from zero to one would be to normalize the measurement such that every area was on the same scale, whatever that scale was. An actual number could be used but then a scale would need to be figured out to translate it into a picture. The measurement itself would be important for determining the outcome of the map but it could measure -- % saturation of cell phones, % users with Interet computers, etc. Next the little squares with E-W land areas could be sorted by range from 0-1 into a line. Now this doesn't look like a map yet but it does provide a start for displaying how close things are. The other dimension could be another arbitrary item including longitude and latitude mixed into a variable that would project a full globe onto a line such that Boston would still be somewhat near Bedford.

I unfortunately don't have the time to make such maps. If you are from Wired Magazine or Time or Princeton and you would like to collaborate with me and give me a team of programmers in Bangalore to create the maps... you'll know where to find me. I am somewhere midway up the cybercone near the US cluster.