After all, in the end, the amount of empirical work we can do is dependent on the energy available (not only our own energy) and the time used per measurement.
First, we may now calculate the cumulative amount of energy received by the Earth since its "creation" and the number of measurements that could hypothetically have been made since this "creation". If we consider the amount of energy we could have spent in measuring to be equivalent to the amount of energy received for the past 4.5 billion years, and using 1.731 X 1017 J.s-1as the value for incoming radiation, this gives a total value of
AE = No. of years X No. of days X No. of hours X No. of seconds X energy s-1
(= 4.5 X109 X 365.3 X 24 X 3600 X 1.7310 X17) (3.4)
Inserting the value of Planck's constant and solving Equation 3.3 we may—again hypothetically—calculate the time necessary for every measurement which will now be
AE 2.5 X1034
Given that the amount resources that can be spent on examining an ecosystem is limited to a finite amount of measurement. For this calculation, a limit is set to 108, an arbitrarily chosen number, which on one hand seems to be very high in terms of field work, but may be rather realistic when processes such as data logging is involved.
Considering number of dependent variables in the system (n) we need at least the in order to determine the full "phase space" we need make at least m, measurements, where m = 3n-1 (2)
This assumes that our knowledge about a given system is so little determined that we have no "a priori" knowledge about the interrelations in the ecosystem, i.e., the physical flows or the regulatory feedbacks in the system. Therefore, we have to assume the worst case—that everything is literally linked to everything. In this case Jorgensen calculates that with the limits of 108 number of measurements we can only deal with a system with fewer than 18 components (as 318 = 387.420.489).
Assuming that our sample is taken from a statistical population with a normal distribution and the standard deviation (a) of the sample mean (x) is given by:
Equation (3.3) may be re-organized into a
Thus, we could possibly make a measurement or sample in 10-67 of a second.
If we could have exercised this practice ever since the creation of the Earth, we could have made 4.7 X 1084 measurements.
Returning to Equation 3.2 this means that we will have standard deviation (SD) (accuracy) of
or in referring to Equation 3.1 we may never succeed in measuring systems with more than n = 237!
To make an intermediate summary there are many ways to express ontic openness. At the same time it has consequences to many relevant aspects of ecology such as the time we use for empirical work as well as the expectations we may have to issues such as accuracy and predictability.
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