A math question for evolutionists., page 1

reply to post by monkcaw

If the age of the Earth and the number of species on it are in any way related, then one could certainly find a mathematical expression for the relationship. Unfortunately, they are not. Catastrophic events produce mass extinctions in particular geographic areas and even on the planet as a whole. There is also a host of other less extreme but equally unpredictable factors affecting the number. We can allow for them statistically, but the result would be a formula that predicted nothing.

However, the thread title and its placement in the Origins & Creation Conspiracy Forum suggests that there may be more to this question than meets the eye. Could it be an attempt to claim that Earth is not old enough to have produced such a vast diversity of species through the mechanism of evolution by natural selection?

If so, it cannot succeed; Earth is more than old enough to have brought forth all her living progeny, and more.

And here is the proof.

Begin with one species.

Assume one successful new speciation event per species every 5,000 generations. I am using the figure 5,000 because in human terms this takes us back roughly 100,000 years (assuming 20 years per generation), and that is more or less the time at which the species Homo sapiens is thought to have originated. If these figures are absurdly wrong, someone with specialist knowledge is most welcome to correct me.

Obviously different species have different life-spans, so the length of time equivalent to 5,000 generations is a variable. Let's call this variable G.

Let the number of species alive on Earth at any time Gn be Sn.

Okay; we're set to go.

Let life first appear on Earth. It consists of one species. At this time G = 0 and S = 1
At G = 1, the first speciation event occurs. S = 2
At G = 2, S = 4...
...and so on. Assuming no extinctions, the number of species doubles every 5,000 generations.
Thus the number of species Sn at G = n is given by the good old geometric progression formula

Sn = S1.Q^(Gn-1)

where S1 =1 and Q, the common ratio, = 2. Therefore

Sn = 2^(Gn - 1)
Now, the first life appeared on Earth about four billion, or 4 x 10^9 years ago.
For the first two billion years or so, the only life around was single-celled and probably didn't survive longer than a couple of days. Let's say five days. That gives us

{2 x 10^9}{365/5}

or roughly 1.5 x 10^11 generations.
Therefore, G for the first two billion years (let's call this Ga) =

{1.5 x 10^11}/{5 x 10^3}

= 1.5/5 x 10^8

= 3 x 10^7 or 30 million.
Now by our formula Sn = 2^(Gn - 1),

Sn = 2^29,999,999

or (writing in longhand, so to speak) a grand total of

200,000,000,000,000,000,000,000,000,000 species

And guess what, kids, we haven't even got to the Cambrian yet. There's a whole 'nother two million years to go...

Of course, this ridiculously large number of species never existed. All species become extinct sooner or later; only a select few survive what Darwin called the winnow of nature. But - even allowing for enormous errors of estimation - it is clear that there has been ample time, not only for the evolution of the 1.75 million species that now live on Earth, but also for all the species that have gone extinct, including the three Great Dyings (Precambrian, Permian and Cretaceous) in which large fractions of all living species were extinguished.

[edit on 19-1-2009 by Astyanax]