It could (and has) also happened under finite time and finite combinations.
Under early earth conditions (best of our knowledge) and given the mechanisms of evolution and the time involved, there is good reason to believe an intelligence is responsible for many historical occurrences:
Gee, really? What are those "good reasons"?
Warning: Alleged arguments *against* evolutionary origins are *not* reasons *for* concluding that "an intelligence is responsible". Epistemology doesn't work that way. Be sure that your answer actually constitutes reasons *for* your particular hypothesis of "an intelligence is responsible". Good luck with that one.
Also, in your answer, please explain the origin of your alleged "responsible intelligence" -- did *it* originate spontaneously by some natural process? If so, why not us? And if it *didn't* originate naturally, is it turtles all the way down then?
"Solving" the riddle of the existence of life and intelligence by postulating *another* pre-existing life and intelligence doesn't really "solve" anything, it just kicks the question down the road.
origin of life, establishment of eukaryotes,
What about them? You sort of "forgot" to include your "reasons" for concluding that "an intelligence is responsible" for these.
evolution of the human brain from the chimp brain (time constraints and mechanisms are huge on this one).
Odd, the folks who have spent a lot of time actually studying the amount of genetic difference between us and the chimps, and comparing to the amount of time since our last common ancestor (about six million years) haven't spotted anything that isn't well within the range of expected genetic accumulation rates. Do you know something they don't know? Or are you just stating what you *presume* without a shred of evidence or study to base it on?
Here's what actual *examination* of the genomes (you know, that "evidence" thing) finds:
Looks good to me... The observed mutation rate in the human genome applied over a period of six million years is more than sufficient to account for the actual amount of genetic divergence found between the human and chimp genomes. If you have evidence to the contrary, *now* would be the time to present it.Prediction 5.8: Genetic rates of change
Rates of genetic change, as measured by nucleotide substitutions, must also be consistent with the rate required from the time allowed in the fossil record and the sequence differences observed between species.
Confirmation:
What we must compare are the data from three independent sources: (1) fossil record estimates of the time of divergence of species, (2) nucleotide differences between species, and (3) the observed rates of mutation in modern species. The overall conclusion is that these three are entirely consistent with one another.
For example, consider the human/chimp divergence, one of the most well-studied evolutionary relationships. Chimpanzees and humans are thought to have diverged, or shared a common ancestor, about 6 Mya, based on the fossil record (Stewart and Disotell 1998). The genomes of chimpanzees and humans are very similar; their DNA sequences overall are 98% identical (King and Wilson 1975; Sverdlov 2000). The greatest differences between these genomes are found in pseudogenes, non-translated sequences, and fourfold degenerate third-base codon positions. All of these are very free from selection constraints, since changes in them have virtually no functional or phenotypic effect, and thus most mutational changes are incorporated and retained in their sequences. For these reasons, they should represent the background rate of spontaneous mutation in the genome. These regions with the highest sequence dissimilarity are what should be compared between species, since they will provide an upper limit on the rate of evolutionary change.
Given a divergence date of 6 Mya, the maximum inferred rate of nucleotide substitution in the most divergent regions of DNA in humans and chimps is ~1.3 x 10-9 base substitutions per site per year. Given a generation time of 15-20 years, this is equivalent to a substitution rate of ~2 x 10-8 per site per generation (Crowe 1993; Futuyma 1998, p. 273).
Background spontaneous mutation rates are extremely important for cancer research, and they have been studied extensively in humans. A review of the spontaneous mutation rate observed in several genes in humans has found an average background mutation rate of 1-5 x 10-8 base substitutions per site per generation. This rate is a very minimum, because its value does not include insertions, deletions, or other base substitution mutations that can destroy the function of these genes (Giannelli et al. 1999; Mohrenweiser 1994, pp. 128-129). Thus, the fit amongst these three independent sources of data is extremely impressive.
Similar results have been found for many other species (Kumar and Subramanian 2002; Li 1997, pp. 180-181, 191). In short, the observed genetic rates of mutation closely match inferred rates based on paleological divergence times and genetic genomic differences. Therefore, the observed rates of mutation can easily account for the genetic differences observed between species as different as mice, chimpanzees, and humans.
Potential Falsification:
It is entirely plausible that measured genetic mutation rates from observations of modern organisms could be orders of magnitude less than that required by rates inferred from the fossil record and sequence divergence.
And for more divergence analyses than you can shake a stick at, see: Initial sequence of the chimpanzee genome and comparison with the human genome. In it you'll find tables like this:
The first interesting thing of note is that there is far *less* genetic divergence between humans and chimps than there is between mice and rats... But I digress.
The table shows the fraction of diverged basepairs in protein-coding genes. Multiple the numbers in the first two rows by 100 if you find percentages more clear.
KS is the fraction of synonymous basepair substitutions since the last common ancestor (out of all possible synonymous substitutions). This is used as a baseline for mutation/fixation rate, since synonymous substitutions are demonstrably neutral in effect, and therefore unaffected by selection.
KA is the fraction of non-synonymous basepair substitutions since the last common ancestor (out of all possible nonsynonymous substutions). These are the mutations that "matter", because they actually make a change in the amino-acid sequence of the protein which the gene produces.
KA/KS is the ratio of the above two numbers, and indicates the fraction of nonsynonymous mutations which fix in the genome relative to the number of synonymous mutations which fix. This indicates the fraction of "meaningful" mutations which end up in the genome, and shows the effect of natural (and other kinds) of evolutionary selection. I'm oversimplifying here, but the ~0.2 ratio for hominids indicates roughly that four out of five mutations in nonsynonymous loci were harmful and weeded out by natural selection, whereas one out of five mutations were neutral or beneficial. (Actually, a more realistic scenario is that more than 4/5 of mutations were harmful, but beneficial mutations which were rarer than 1/5 were strongly positively selected, resulting in an overall average fixation rate of 1/5.)
For the current discussion, however, the most relevant number is KS. This is the figure which you allege is too high to be plausibly possible within six million years. But is it really? For a 20-year generation time (too long for most of hominid history, but let's be conservative in our estimate) over 6MY, that means .00617 / 6M * 20 = 2.06 x 10-8 mutations per generation at a given locus is needed in order to generate the observed genetic divergence between chimps and humans.
As the above quoted material already establishes, the observed mutation rate for humans is on the order of 1 to 5 x 10-8 mutations per generation per locus. So the *observed* mutation rate in humans is pretty much exactly equal to the amount of divergence found between humans and chimps. Looks good to me, how about you? So what's that you were saying about "time constraints are huge" on the human/chimp divergence? On the contrary, the amount of time it has taken seems just about exactly right.
Ah, but you may point out, these are just the average divergences, what's the story on the greatest-diverging nonsynonymous changes in genes? I'm glad you asked. Here are the "most diverged" genes between humans and chimps:
Bad news for the folks who presume that brain differences are going to be the biggest genetic differences between humans and chimps: Unless I'm missing something I don't see any brain-related genes on the top 16 most-changed genes, but instead we find a lot of genes relating to hair/skin/nails, smell/taste, and the immune system. Fascinating. And that's not just an evolution-based finding -- even if some unspecified "designer" built those genomes, he/she/it still found the need to craft larger differences in the genes which regulate hair/skin/nails and so on than the ones which directly regulate brain developement and activity.
Location (human) Cluster Median KA/KI* *Maximum median KA/KI if the cluster stretched over more than one window of ten genes.
1q21 Epidermal differentiation complex 1.46 6p22 Olfactory receptors and HLA-A 0.96 20p11 Cystatins 0.94 19q13 Pregnancy-specific glycoproteins 0.94 17q21 Hair keratins and keratin-associated proteins 0.93 19q13 CD33-related Siglecs 0.90 20q13 WAP domain protease inhibitors 0.90 22q11 Immunoglobulin- /breakpoint critical region
0.85 12p13 Taste receptors, type 2 0.81 17q12 Chemokine (C-C motif) ligands 0.81 19q13 Leukocyte-associated immunoglobulin-like receptors 0.80 5q31 Protocadherin- 0.77 1q32 Complement component 4-binding proteins 0.76 21q22 Keratin-associated proteins and uncharacterized ORFs 0.76 1q23 CD1 antigens 0.72 4q13 Chemokine (C-X-C motif) ligands 0.70
Look, go for it -- there are several databases online where you can peruse the complete genomes of both chimp and man. Feel free to point out the gene or genes which you feel are so different between the two that ordinary rates of mutation and genetic fixation aren't statistically sufficient to account for the differences. We'll wait.