1:30 – 4:00 School. Rain, rain, rain.

• Continuing with Sociophysics
  • 6.5 Is it really a small world? Searching post Milgram
    • 6.5.8 Funneling properties.
      • The funneling capability of a node can be defined as the fraction of successful dynamic paths through it when the target is fixed and the source is varied. Two thoughts: First, this seems to be a measurement of centrality. Second, Large, vague nodes are needed for ‘laundering’ information into misinformation or conspiracy theory.
      • Consider four agents. Who have characteristics that can vary between (0, 1).
        • Agent 1 has two color intensities: R=0.1, G= 0.7
        • Agent 2 has one color and two note volumes R=0.3, A=0.2, F=0.6
        • Agent 3 also has one color and two note volumes B=0.4, D=1, E=0.2
        • Agent 4 has three notes A=0.3, D=0.4, E=0.5
      • Let’s assume that funneling is not required if agents share a color or note. This means that A4 can get to A1 through A2, but A3 has to get to A1 via A4 and then A2. In a matrix this looks like

      	R	G	B	A	D	E	F
      Agent1	0.1	0.7
      Agent2	0.3			0.2			0.6
      Agent3			0.4		1.0	0.2
      Agent4				0.3	0.4	0.5

      • But if we add the hypernyms Color and Notes, we can get funneling. I am summing the color and notes to give a sense of the agent’s ‘projection’ into the larger, more general space. I think the ‘size’ of the funnels are the number of items that go in them times the range of each item. So Color would have a range of (0, 3) and Notes would have a range of (0, 4), since I’m not including B, C, and G here:

      	R	G	B	A	D	E	F	Color	Notes
      Agent1	0.1	0.7						0.8
      Agent2	0.3			0.2			0.6	0.3	0.8
      Agent3			0.4		1.0	0.2		0.4	1.2
      Agent4				0.3	0.4	0.5			1.2

      • Now agents 2 and 3 can get to each other through either Color or note in two hops, and the Agents 1 and 4 can reach each other by going through each of the funnels.
      • There should be a cost in using a funnel though. You loose the information about which color or which note. Intuitively, a series of steps with non-funnel links should be somehow more specific than the same number of steps through a funnel.
      • Practical uses would be a way to detect poorly reasoned conclusions, as long as the beginning and end of the train of thought could be identified.
  • Knowing a network by walking on it: emergence of scaling (Alexei Vázquez) Looks like an interesting guy with a wide range of publications.