Why are we not digging up half-man/half-apes and half-reptile/half-birds?
We do indeed find many transitions between both of those group-pairs.
Your question is based on the false premise that we do not.
Why aren't the necessary transitional forms required for evolution to be true there to be found?
Few creatures fossilize, so the likelyhood of there being and us finding the fossil remains of every generation in a line of evolution are staggeringly unlikely.
Why is nature not in chaos but rather well-ordered if spontaneous random processes are ongoing?
There are several false premises here.
You ask why nature is not in chaos: Nature is chaotic.
You ask why the existance of random processes does not prevent order: Processes are not random.
Easy to say, but there are few definite examples.
ftp://ftp.winitzer-family.net/Htdocs/Jerry/images/hominids2_big.jpg
Where are they being "found quite often"?
In the ground
Why aren't these magnificent incontrovertible proofs of evolution being rammed down our throats daily, everywhere?
No money in it. They are redily available to anyone that looks.
Just because you're convinced its so, doesn't make it so I'm afraid.
No, but because the ecidence clearly proves it so is why I'm convinced.
Speciation occurs quickly on a geological timescale?
No, speciation is observed on record:
Two strains of Drosophila paulistorum developed hybrid sterility of male offspring between 1958 and 1963. Artificial selection induced strong intra-strain mating preferences. (Test for speciation: sterile offspring and lack of interbreeding affinity.) Dobzhansky, Th., and O. Pavlovsky, 1971. "An experimentally created incipient species of Drosophila", Nature 23:289-292
Rapid speciation of the Faeroe Island house mouse, which occurred in less than 250 years after man brought the creature to the island. (Test for speciation in this case is based on morphology. It is unlikely that forced breeding experiments have been performed with the parent stock.) Stanley, S., 1979. Macroevolution: Pattern and Process, San Francisco, W.H. Freeman and Company. p. 41
Formation of five new species of cichlid fishes which formed since they were isolated less than 4000 years ago from the parent stock, Lake Nagubago. (Test for speciation in this case is by morphology and lack of natural interbreeding. These fish have complex mating rituals and different coloration. While it might be possible that different species are inter-fertile, they cannot be convinced to mate.) Mayr, E., 1970. Populations, Species, and Evolution, Massachusetts, Harvard University Press. p. 348
page 22 of the February, 1989 issue of Scientific American. It's called "A Breed Apart." It tells about studies conducted on a fruit fly, Rhagoletis pomonella, that is a parasite of the hawthorn tree and its fruit, which is commonly called the thorn apple. About 150 years ago, some of these flies began infesting apple trees, as well. The flies feed an breed on either apples or thorn apples, but not both. There's enough evidence to convince the scientific investigators that they're witnessing speciation in action. Note that some of the investigators set out to prove that speciation was not happening; the evidence convinced them otherwise.
Goatsbeard ("Three species of wildflowers called goatsbeards were introduced to the United States from Europe shortly after the turn of the century. Within a few decades their populations expanded and began to encounter one another in the American West. Whenever mixed populations occurred, the specied interbred (hybridizing) producing sterile hybrid offspring. Suddenly, in the late forties two new species of goatsbeard appeared near Pullman, Washington. Although the new species were similar in appearance to the hybrids, they produced fertile offspring. The evolutionary process had created a separate species that could reproduce but not mate with the goatsbeard plants from which it had evolved.")
Then there's our wolf-turned-parasite.
THAT's the reason no-one's found any remains of transitional forms! Of course...
False premise. Everthing ever found is a transistional form (unless it had no offspring).
Archaeopteryx is the most primitve and earliest known species of bird, but it's debated to this day whether its characteristics have anything to do with reptiles.
That's not true either. Some distinclty reptile features of archaeopteryx:
Premaxilla and maxilla are not horn-covered
Trunk region vertebra are free.
Pubic shafts with a plate-like, and slightly angled transverse cross-section
Cerebral hemispheres elongate, slender and cerebellum is situated behind the mid-brain and doesn't overlap it from behind or press down on it.
Neck attaches to skull from the rear as in dinosaurs not from below as in modern birds.
Center of cervical vertebrae have simple concave articular facets.
Long bony tail with many free vertebrae up to tip (no pygostyle).
Premaxilla and maxilla bones bear teeth.
Ribs slender, without joints or uncinate processes and do not articulate with the sternum.
Pelvic girdle and femur joint is archosaurian rather than avian (except for the backward pointing pubis as mentioned above)
The Sacrum (the vertebrae developed for the attachment of pelvic girdle) occupies 6 vertebra.
Metacarpals (hand) free (except 3rd metacarpal), wrist hand joint flexible.
Nasal opening far forward, separated from the eye by a large preorbital fenestra (hole).
Deltoid ridge of the humerus faces anteriorly as do the radial and ulnar condyles.
Claws on 3 unfused digits.
The fibula is equal in length to the tibia in the leg.
Metatarsals (foot bones) free.
Gastralia present.
There's about 22 features not found in birds taht are foudn in both reptiles and arch.
Rubbish, I've been in quite a few more serious debates with people far more knowlegable about the subject than you, sir.
This is simple posturing. Your posts show a distinct ignorance to the basic facts being discussed. Almost every point in them is based on a demonstrably incorrect premise (as I've expanded on in this post here).
