A MATHEMATICAL CRITIQUE
of the “open space”
This website constitutes a mathematical critique that underscores the deeply-erroneous nature of such
"open space" hypotheses.
Since marine biologists routinely sample one-liter samples of red-tide outbreaks, the following data provide
a starting point for a mathematical portrait: First, severe and deadly red-tide
conditions are common when K. brevis populations reach concentrations of between 10,000 to
1,000,000 or more cells per liter.
Secondly, a one-liter sample of water equals approximately 61.024 cubic inches.
And thirdly, we will utilize the dimensions of a typical cell of K. brevis are
also shown below.
volume of 1 liter = 61.024 cubic inches
Dimensions of a typical cell of K. brevis
personal communication, 2008; floridamarine.org 2008)
L: ~30 um (= 0.03 mm) = ~ 0.0012 inches
W: ~ 0.0014 inches (“a little wider than it is long" – floridamarine.org)
D: ~ 10 – 15
um deep (10 um = .0004; 15 um = .0006), so average = ~ .0005 inches
The data above allow us to make the following calculations:
Volume of a typical cell of K. brevis = (L) x (W) x (D)
= (.0012) x (.0014) x (.0005)
= ~ .000 000 000 840 cubic inches
Therefore, one million K. brevis cells occupy approximately
(1,000,000) x (.000 000 000 840), or an actual physical volume
of approximately .000 84 cubic inches
Since one liter equals 61.024 cubic inches, subtracting 00.000 84 cubic inches occupied by the cells of
K. brevis leaves (61.024) – (00.000 84) = approximately 61.023 16 cubic inches
In other words, the dinoflagellates in this liter of water still have
approximately 61.023 16 cubic inches
of unoccupied volume (of apparently“ empty space”) still remaining theoretically-available
= (61.023 16) divided by (61.024 00)
= ~ .999 987 2
= ~ 99.998 72 % unoccupied
This means that the above dinoflagellate population manages
to routinely visit calamity upon themselves and the aqueous environment in which they live even when they physically-occupy less than two one-thousandths of one
percent) of the total volume that seems to remain theoretically-available to them.
(100%) – (99.998 72%) =
.001 28 %
or less than two one-thousandths of one percent
of the volume that seems to remain theoretically-available to them
In other words, despite an apparently enormous amount of open
space, and despite the fact that the Karenia
brevis population occupies a "volumetrically-insignificant" portion of the remaining “open space” that
seems to be available,
they have, by their combined overpopulation and their
of unseen, invisible, and calamitous wastes
the watery surroundings in which they live.