* Supporting Mathematics*

A MATHEMATICAL CRITIQUE

*of the “open space”
hypothesis*

PART ONE

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.

**Background values:**

A
volume of 1 liter = 61.024 cubic inches

Dimensions of a typical cell of *K. brevis *

(Nierenberg,
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
*still unoccupied*

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
to them.

**Percentage unoccupied**

= (61.023 16) divided by (61.024 00)

= ~ .999 987 2

= ~ 99.998 72 %** unoccupied**

**volume remaining**

* *

*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

production
of __unseen, invisible, and calamitous wastes__

__catastrophically-damaged
the watery surroundings in which they live.__