would think, what with the networking capabilities we have, that 6 will reduce...
SimSim, Aug 14, 2008 @ 09:40

We have our own Kevin Bacon in the form of Julian Thompson here in the Geneva area. I have a JT score of one as he's on my friends list.
britabroad, Aug 14, 2008 @ 11:13

Hi



its not 100% true, the study performed by Microsoft is using the internet and they concluded that an complete connection graph is 6.7 nodes, which means you are 6.7 person away from anybody who is connected to the internet.



So the correct should be "7 degrees of separation on the internet" but the question is if it apply to the world (not the internet).

- SPAM, it will connect people who dont know each other

- Large populations who dont have access to the internet.



For example there has been done statistic over the US population and some result has come to that only 2-3 links are needed, but they we have to determine what a link is

- Strong link, you know the person and you can call him/here in the middle of the night.

- Week link, you would say "Hi" but never interact.

and these reseachers argued that only 1-2 more links needed to connect the whole world, which would mean "3-5 degrees of separation" but other mathematicians who use population statistic says we probably are talking about 8 degrees of separation (and that is a lot...).



If we look at the difference in separation, now this is the number of people our network will contain if we want to reach the farthest person



4 degree = 256 people

5 degree = 3 125 people

6 degree = 46 656 people

7 degree = 823 543 people

8 degree = 16 777 216 people

9 degree = 387 420 489 people

10 degree = 10 000 000 000 people (almost double the world population)

11 degree = 285 311 670 611 people



and if we look at this, it is quite logical that the human connection graph should be around 7, using slight under 1 million of people, and because we are 6.5 billion people we are 100% connected with less then 10 degrees if we only know 1 person



its a nice thought, but not really shocking when you understand the math behind it, it has to be around 6-8 but its a very huge difference between 6 or 8. The problem is that its very very hard to prove, the graph can easily be constructed and calculated but getting the data (how people know and interact) is much harder and I would say almost impossible.
sandholm, Aug 14, 2008 @ 11:15

Hi,



It's not necessarily true that "you are linked by a string of approximately 6 acquaintances to Noam Chomsky or Tiger Woods." As you rightly say, on average it's 6 degrees of separation (i.e., between an arbitrary pair of people), but to any one person it may be as many as 29 (or even more) links, as the article states.



It's funny how this topic still frequently pops up as cocktail party or forum discussion :P The mathematics of it has been studied extensively though, and the phenomenon is known as a "small world network", formalized and made popular in particular by Duncan Watts (a crazy and very smart Australian guy and former colleague at the Santa Fe Institute, now at Colombia University). See the following links for more info if you're really interested in this stuff:



Small world networks

Duncan's book



Best,



Wim

wim_in_ch, Aug 14, 2008 @ 13:01

Hi,

Yes, at the beginning I wrote  "The fascinating theory of six degrees of separation contends that any two strangers on the planet are, on average, distanced by  approximately 6 degrees of separation, because we are all linked by chains of acquaintance " in order to clarify that it's a matter of statistics: we work with average values but the real values can be in fact more or less far from the average value. 

By taking it into account, I wrote that "you are linked by a string of approximately 6 acquaintances to Noam Chomsky or Tiger Woods" which meant that the real value could be more or less far from 6.

But those are questions of style and words and the most important, I think, is this interesting question about the chains of acquaintance.

As Sandholm wrote, if we think a little bit about this issue, we find other questions: can an internet based experiment inform us about what happens in the "real world"? What's a "real world"? Are there connections that are more "real" than others?, etc... :w00t:
new_concept, Aug 14, 2008 @ 15:14

Sure, it's a matter of wording, but I wouldn't consider 29 to be approximately 6 ;)



Anyway, the main point is that the work on small world networks has already answered many of these "interesting questions", and in many cases by using some relatively simple maths. And it doesn't matter if a world or network is "real" or not (in whatever sense), cos the whole point of these small world networks is that they show up everywhere: on the (unreal?) internet, in "normal" social networks, in collaboration networks (such as between movie stars, or scientists), but also in ecological networks, gene networks, and almost any kind of network you can find in the world!



"2 is not equal to 3, not even for large values of 2." :hehe:



Wim

wim_in_ch, Aug 14, 2008 @ 15:27

" Anyway, the main point is that the work on small world networks has already answered many of these "interesting questions", and in many cases by using some relatively simple maths. And it doesn't matter if a world or network is "real" or not (in whatever sense), cos the whole point of these small world networks is that they show up everywhere: on the (unreal?) internet, in "normal" social networks, in collaboration networks (such as between movie stars, or scientists), but also in ecological networks, gene networks, and almost any kind of network you can find in the world! ".

Yes, I agree with the fact that some reduced systems can show what happens in a more important systems if both have some commom properties: that is one of the basis of statistics.

But we can always wonder (as a philosophical inquiry) what are the basis (if they exist!) of thoses correspondances between small and important systems.

new_concept, Aug 15, 2008 @ 00:39

True, the philosophical questions are always there and worth pondering.



Although I actually believe that even those are being addressed and answered quite adequately these days by the theories of complex systems and emergence. The evidence is rather overwhelming that all these different systems (small and large) actually do indeed have the same basic underlying principles. So in that sense it is perhaps not that surprising after all that seemingly different systems like the internet, the brain, and ant colonies, actually operate in very similar ways and show the same kind of properties and behaviors. :w00t:



It's all fascinating stuff, and it's always fun to see these topics popping up in non-scientific contexts... ;)



(And, btw, thanks for that link to the article!)



Cheers,



Wim

wim_in_ch, Aug 15, 2008 @ 11:53