New World Record OW Swim

draw or imagine several squares, three inches on each side. draw an equal number of horizontal and vertical lines to create small squares, as in tic-tac-toe. in one square draw 10 horizontal and 10 vertical to yield 100 squares. leave one blank. divide the others as you like. now draw a dotted horizontal line form one side to the other, in each of the three inch squares. each small square represents one shark. each big square represent an ocean region and has the given population density. the dotted line represents pennys swim. when the shark population density is 100 per big-square, then she encounters 10 sharks. when the population drops to 1%, then she encounters only one shark. this is a 100-fold change in population density, but only a ten-fold change in shark-sightings if the population changes x-fold, then the sightings change by the square root of x. but this is just a naive model of 'counting sharks along a transect'. i'm guessing it sets a lower bound, and that penny's transect had a fractional dimension between 1 and 2. I think depends on the 'width' of penny's transect relative to the shark population density, as well as some statistical refinements. While averaging out sharks over a square area is helpful, a statistical evaluation would better reflect a real world analysis. So I would suggest that in any 100 X 100 square mile area, you could have all the sharks hovering in the path of Penny, or absolutely none. It is equally probable as any other given distribution so long as you identify each shark as a unique element of the statistical evaluation rather than referring to is a a generic shark. This also assumes that the sharks are neither attracted to a swimmer surrounded by 2 65 ft boats, 2 Zodiacs and 2 kayakers, nor scared off by them.

draw or imagine several squares, three inches on each side. draw an equal number of horizontal and vertical lines to create small squares, as in tic-tac-toe. in one square draw 10 horizontal and 10 vertical to yield 100 squares. leave one blank. divide the others as you like. now draw a dotted horizontal line form one side to the other, in each of the three inch squares. each small square represents one shark. each big square represent an ocean region and has the given population density. the dotted line represents pennys swim. when the shark population density is 100 per big-square, then she encounters 10 sharks. when the population drops to 1%, then she encounters only one shark. this is a 100-fold change in population density, but only a ten-fold change in shark-sightings if the population changes x-fold, then the sightings change by the square root of x. but this is just a naive model of 'counting sharks along a transect'. i'm guessing it sets a lower bound, and that penny's transect had a fractional dimension between 1 and 2. I think depends on the 'width' of penny's transect relative to the shark population density, as well as some statistical refinements. While averaging out sharks over a square area is helpful, a statistical evaluation would better reflect a real world analysis. So I would suggest that in any 100 X 100 square mile area, you could have all the sharks hovering in the path of Penny, or absolutely none. It is equally probable as any other given distribution so long as you identify each shark as a unique element of the statistical evaluation rather than referring to is a a generic shark. This also assumes that the sharks are neither attracted to a swimmer surrounded by 2 65 ft boats, 2 Zodiacs and 2 kayakers, nor scared off by them.