Radioactive decay is an ironclad law of physics that has remained constant over the last 14 billion years. The constancy of this law was verified when I showed, in my very first post, that one can calculate the expected concentration of the elements created in the first 4 minutes after the Big Bang even though the temperature at those conditions were billions of degree Kelvin to millions of degree Kelvin.
And these predictions, made from the laws of physics alone so far back in time and under such extreme conditions have been validated by observations.
In contrast, there is no
constant laws of physics in the mathematics of population growth and decay. Population growth rate is determined by the logistics equation. If N is the population at a given time then:-
Rate of Population Growth (dN/dt) = r*N where r is the intrinsic rate of population increase given by r = log(R) where R is the number of offsprings per individual in the population.
This gives us an exponentially increasing rate of population growth, but only when there is no constraints on food, living space, disease and predation, and other resources. Thus the intrinsic rate itself varies depending on both the environment and the population size.
The maximum number of adults of a species that a habitat can support is called it carrying capacity and is called K. This gives us the actual growth equation called the
logistic equation:-
dN/dt = r*N*[(K-N)/K]
where (K-N)/K is the fraction of the environment that can still be exploited to sustain additional adults.
Thus for a given value of K, one gets a typical S shaped curve of population with time. Here is an example for the population growth and stabilization of insect population in an environment with limited food. Note how peak population scales with carrying capacity.
Human beings, by their technology and medicine and agricultural advancements have repeatedly increased the degree to which they can exploit natural resources and hence increased the carrying capacity K. The carrying capacity has increased over several episodes in human history (agricultural revolution, urbanization and finally industrial revolution) and human growth rate has followed the expected logistic curve associated with each increase in K.
Thus, as you can see, we know what controls population growth rates, why it is not linear or constant and we can use the validated mathematical theories appropriate for population dynamics to predict and explain population growths that we see in either human society or in ecology.
There is no analogy that can be drawn between radioactive decay rates and population growth and collapse rates. Both are well explained through DIFFERENT but well validated theories of science (one physics, the other ecology).
So...how do you justify drawing parallels between the two when science shows that they have no similarity?
Instead of making claims that there exists some "startling facts", please present them here so that we can have a discussion.
No. There has been no extrapolation whatsoever. I have provided actual
observational evidence that demonstrates the constancy of the laws of physics
under very very extreme temperature and pressure ranges of early Big Bang environments (more extreme than the interior of sun). Even millions of Kelvins of temperature have been shown to be not enough to alter these laws of physics. But, more than that, since a basalt rock will simply melt at temperatures between 1000 C and 600 C, and since the time being measured
is the time since last solidification i.e. the time since that specific rock and crystals within it have not been subjected to temperatures more than 500 C, which is very modest and has no effect whatsoever in decay constants. So, for example, rocks that were directly hit by a large meteorite (or an atomic bomb) would simply vaporize away. Once they condense out into new rocks, the time in these rocks will be time since they condensed back and hence will be from after the catastrophic vaporization event.
So no, what you are proposing has not happened to these rocks that are being dated by radiometric techniques.