Posted by Hans on December 01, 2003 at 06:16:42:
In Reply to: Re: And then there was one... (A different version of the graph) posted by stmx3 on November 26, 2003 at 06:03:09:
If you are referring to the vaguely M shaped form to the peaks round about generation 9, I suspect this is an artifact of MS Excel's (or whatever charting program was used) smoothing function. I think if you presented the data as a histogram, this dip would be much less pronounced, if not disappear altogether. The main reason I suspect this is because Phil clearly states he has set the maximum at 1, yet the curve goes above one on either side of generation 9.
If you are talking about some other feature of the chart, then ignore this, because I'm not certain what you are refering to.
: : : Very interesting graph. Any thoughts as to why there is a dip in the center of the peak? Seems to be consistent throughout the number of votes.
: : Best guess, natural variation. With as 'few' as 1200 items spread acress just 16 generations, chances are that, whatever general formula or trend spreads them around, there's going to be a visible anomaly or two somewhere on the graph through chance (similarly with the wobble on the way 'up' to the peaks from the lower Gens).
: : You'll see the lefthand peak has gotten eroded away for the latest line (the near-white one), or else the peak and pre-peak (ex-dip) numbers were reinforced to out-pace it (the prior post's graph, with absolute figures, suggests a bit of both).
: : The other off-peak wobbles are more pronounced, with the latest line, but not to any level of statistical importance, I would hazard to say.
: I would bet that if you made a time lapse movie of this graph, you would see the wobbles migrate from left to right across the generations. I think it would look like ripples on a pond. Even now, with the latest line, there is a wobble on the right side of the peak. I interpret these "wobbles" as regions of local stability due to some phrase that arose and is achieving longevity in its generation while passing it on to subsequent generations.
: But not only would you see a movement of the wobble across the graph (to be perhaps dampened out at the peak...or absorbed into the peak, thereby raising the height of the peak), but you would see the wobble causes the peak to move to the right a bit. Think of the peak as some stationary mass. Then the wobble is like some impetus...or a force acting to push the mass to the right.
: Also you would see spontaneous production of a wobble due to genetic variations or mutations which give rise to another stable phrase. I think this is the reason for the wobble to the right of the peak. Since everything must continually move to the right, I bet this wobble will form a second peak to the right of the main peak, albeit somewhat smaller, and you would find you have something like a camel back hump.
: I don't know how often you collect data, but if one could make a short movie of this graph, I think you might find some interesting "physics" in there.