[P]ointing out where your math is wrong. You said: The other variable involved… is 5,000,000,000,000 cells. As I have already pointed out, that is a meaningless number. It is not a “variable” that can be applied to the chances or regularity of mutations. The largest Blue Whale today has 100 quadrillion cells. Quite the number, yes? Diplodocus’s [Eds. note: sic] had many, many more. Cells are easy. Get the template and it’s just a game of replication to meet the need. Big lungs, small lungs, it doesn’t matter. And I remind you, you then said that is five trillion pieces of genetic code that need to be affected, in order to transform those lungs, over four billion years, from ocean-respirating lungs to air-respirating lungs. Errrum, no. Dead, dead, dead wrong. The mutation need only occur in one cell...
High Arka responds:
You're correct that many different cells can be made from the "template" in the DNA. Good show! What you're not understanding, though, is that there are many different types of cells in the body. These cells generally correspond to a number of complex bodily systems. For example: the "cardiovascular system," or the "nervous system." (These systems are all integrated, and the distinction is an artificial one, but it serves a differential purpose for our discussion, here.)
Within these "systems," there are subdivisions of smaller systems, such as the limbic system within the nervous system. Within those sub-systems, there are sometimes other sub-sub-systems, and within those components, at a lower scale, we reach the cells themselves. (DNA also encodes the designs for intra-cellular components, as well as their placement, but we'll keep things simple and stick to just the level of "the cell," for now.)
Now, you're correct that those cells are made from a "template" in the DNA. However, the production of a type of cell is only one of the pieces of information that the DNA includes regarding that cell.
The DNA templates for the nervous system include the cells that make up the different sub-systems and other materials found inside various parts of the nervous system. This includes cell placement, which is why the total mass of the organism is of great importance in considering cellular sequence mutation. For example, the nervous system includes, among other things:
1) Glial cells;
2) Myelinated nerve cells and myelinated axons;
4) Capillary endothelial cells.
Now, the glial cells appear in both white matter and gray matter, where they help to process cognitive functions. However, they need to be very specifically located in order to achieve this task. A bicycle, for example, can help a person travel faster--but only if that person is on the bicycle. If the bicycle is located a mile away, the bicycle cannot be used to help that person travel faster.
An organism's DNA provides information relevant to the growth of the proper kind of cell--such as the capillary endothelial cells that appear in cerebrospinal fluid--but also to the proper placement of that cell within the organism. The result of this is that cerebrospinal fluid tends to appear in the spine, cushioning the brain inside the skull, and other appropriate places--but not in sacs growing from your toenails. Whereas cerebrospinal fluid is vital for life inside your spine and your brain-case, it could be deadly if it were being produced in other areas of your body--such as your bone marrow, your heart, or your lungs. Or your kidneys, or your liver, or your appendix, etc.
These adjustments to positioning are delicate things to manage, because even a single inch of deviation can mean the difference between cerebrospinal fluid passing safely through the vertebrae, or filling the chest cavity and killing the organism.
Every mutation which happens to a germ-line during reproduction, therefore, in order to produce a successful offspring, has to include information for the proper positioning of the cell. Not only would a lung cell sequence have to mutate so as to begin producing certain kinds of new cells, it would have to mutate so as to position those new cells in the proper places. Were the cells improperly positioned, they would interfere with the operation of other cells, and be, essentially, a tumor.
Smaller, simpler organisms can evolve faster as a result of this. That is why the evolution of, say, e.coli, is much easier to study than the evolution of, say, elephants. Or diplodocuses.
I know it seems like a wonderfully simple, elegant explanation for you to think, "All it takes is a small change in the DNA!" In actuality, the DNA contains much, more more information than "how to make cells." It specifies where to make them, as we've discussed in more detail here. It also specifies when to make them. E.g., certain hormones appear during infancy, during childhood, during puberty, at menopause, etc. A vast amount of information is included in those sequences. A small adrenal adjustment timed to appear during infancy would kill a baby boy, whereas its absence during puberty would prevent adult development.
(DNA also encodes information about cell quantity, e.g., how many of a certain type of cell to produce. This is why some people are little people and some people are 6'10". It's also why any given diplodocus grows to a certain size, rather than becoming a super-diplodocus, a mini-diplodocus, et cetera.)
When that information goes wrong in certain ways, we call it cancer. Cells that appear in the wrong places, or that reproduce at an improper rate, draw resources from the rest of the body, interfere with the operation of other systems, and frequently cripple or kill their hosts. In order for Alexandra to properly evolve from water-breathing lungs to air-breathing lungs, she has to ensure that the reproductive cycles discussed in Expressed Mathematics of Germ-Line Mutations results not only in the gradual replacement of the water-breathing lung by the air-breathing lung, but also the lack of insertion of any of the lung cells into other bodily systems, or the invasion of the lung by any non-lung cells that would kill the resulting generations of Alexandras.
If you're inclined to foreshadowing, take a look at cancer (or "autoimmune diseases," lol) for just that reason: cancer is real evolution--coordinated evolution--happening between an industrially poisoned ecosystem and the pre-industrial bodies still living in that ecosystem. Cancer amazes us with its swiftness in overtaking our population and coordinating with our environmental and lifestyle choices because we've been led to believe that evolution is a slow, random process, rather than one of continual feedback with the planetary system from which these bodies grew. Before our very eyes, we're seeing our bodies begin to evolve new internal systems for processing abundant post-industrial toxins--the replacement of one type of lightform with another.
Enjoy your trip. I know I have.