Cloudscape

A zygote differentiates into an embryo and then into a fetus through epigenesis, a process in which certain chemical reactions within different cells turn certain genes on or off. At one place, the embryo will turn on genes for the hands, at another for the lungs, and so forth.
This process happens gradually. The cells first differentiate into an entire system. The cells of this system then differentiate into an organ, and the cells of the organ then differentiate into tissues. When the cells form into a system, all cells in this system are still identical, and the same counts for the cells in the organ as it is first formed.
It would be far too much for the cells to take if they were to give exact specifications for every cell descended from them. Instead, they leave their daughter cells to tell what their daughter cells what to do, which may include in turn telling their daughter cells to do.
It's like the hierarchy of an army. The general cannot give instructions to every soldier, but he can give instructions to the lieutenant generals. Every rank is supported by their superiors. The totipotent stem cells are the generals. The pluripotent and multipotent stem cells are the higher-ranking officers, the oligopotent stem cells are the sergeants, the unipotent stem cells are the corporals, and the non-stem cells are the soldiers.
In this way, the differentiation of the human body works like a fractal, and our DNA is nothing more than the code for a series of intertwining fractals: the operations of the fractal's function is repeated for every cell throughout differentiation, and every operation is a detail of the former. In this the body can be said to be a vastly more complex version of the Mandelbrot set, except that the function of the body's fractals is not just a few characters, but billions of characters long. Of course, there is more to differentiation than those billions of characters, but there is also more to the Mandelbrot set than those few characters, that is, the entire field of complex mathematics.
Who knows, if we had a perfect physics engine, there would be a mathematical function for the human body just as there is for the Mandelbrot set. With the right code, we could actually calculate a simulation of the entire human body. Genetics is but biology's informatics, and like informatics, genetics obeys mathematics, even though those mathematics are subject to the chaos of nature, just as informatics may be subject to the chaos of random number generators.
As the systems and then the organs forms, certain of its cells will lie more toward the outside while others will lie more on the inside. This will result in interacts with the environment which will trigger chemical reactions which will in turn cause differentiation. As the outermost layers of cells differentiate, they will release signaling molecules to other cells which will in turn cause them to differentiate, so that a chain reaction is caused. The same counts for the innermost layers, which will interact with chemicals in the blood vessels. It is also possible that physical pressure, either from the amniotic fluid or the blood, is a cue in differentiation.
Moreover, as the cells differentiate, they will form blood vessels which in turn allow the interaction with blood, which may in turn trigger differentiation, including the formation of angiogenesis, so that, again, a chain reaction is caused.
At the time the zygote becomes a morula, it still doesn't know what cell will become what organ. Even when the morula becomes a blastula, all cells in the inner cell mass are still epigenetically identical, that is to say, all cells have activated the same genes. The only differentiation that has happened so far is that between the inner cell mass and the trophoblast, a single-celled membrane. It is easy for the cells of the blastula to tell if they should differentiate into a trophoblast: they're the cells that lie on the outside. However, at this point, the embryo still can't tell where its head or where its feet will be, and at this point it may be anywhere. When the blastula becomes a blastocyst, it is the endometrium which causes the first signal that breaks the embryo's symmetry: the inner cell mass becomes attracted by signaling molecules secreted by the endometrium. Meanwhile, intercellular communication between the trophoblast and the inner cell mass will cause the two to become detached from one another, so that all cells are gathered near the endometrium.
However, the inner cell mass is still a mass of identical cells. It now knows inside and outside and front from rear, but it knows neither left and right nor up and down. This time, it is the pulse of the mother's blood vessels that delivers the embryo from this dilemma.
Upon implantation, the embryo connects to the mother's circulatory system through arterioles that will later be replaced by the umbilical cord. This is by far the most crucial step in the whole process of differentiation. Up till now, where the head would be could just as well be where the arm would be, because the embryo is symmetrical. Now, suddenly, everything becomes fixed. Below the arteriole, where the pulse is strongest, will be the head, which needs most oxygen, and which will be directed downwards throughout the embryo's and later the fetus' development.
This crucial stage is concurrent with gastrulation: as the embryo connects to the mother's circulation, it will determine the shape of the embryo. The flow of the blood gives the embryo the form of a bean and eventually forms it into a gastrula. At this point, all of a sudden, the base of the body is now fixed, and the cells already know into what systems they are to differentiate. At this point, three germ layers are formed: the ectoderm, the mesoderm and the endoderm. The ectoderm, the outer layer, will later forms the integumentary system and the nervous system, the mesoderm or middle layer will form the bones, muscles, circulatory and excretory systems and the endoderm or inner layer will form the respiratory, digestive and endocrine systems.
The rest is child's play. Now the embryo is no longer symmetrical, it can use its own asymmetry to orient itself. The head and arms will form at the lower end of the embryo, the legs and genitals will form at the other end, and the rest in between. Once it knows where the extremities will be, it has but to align each body part in the mesoderm next to these extremities, upon which it aligns the body parts in the endoderm next to the body parts in the mesoderm.
The embryo can tell which side is up and which is down either through the pulse of the mother, which is weaker when it curves back up to the upper end of the embryo, or, possibly, through a form of gravitropism, or orientation in response to gravity. Gravitropism is normally caused by organelles, so it could certainly be caused in a single cell. Gravitropism has only been observed in plants, but the gravitropism that would take place in an embryo is a different kind than that which occurs in plants. Plants need gravitropism to know in which indirection to grow. Embryos would need gravitropism merely to know what genes to activate, which is a far less complex procedure.
As the fetus grows, it could be that gravity has another important role: because of gravity, more blood and therefore more nutrients collects in the lower part of the fetus, which is the head, which furthers its development. A large part of the fetus' mass is comprised of the head. The head needs to develop faster than the rest of the body because it has no time to fully develop before parturition, and if it does not grow as fast as it can, its fontanels will be too weak upon birth to provide sufficient protection to the brain. The position of the fetus may promote this exceptionally rapid development.
The fetus' is only positioned with the head downward in animals in a standing position, such as humans. In quadripeds, it is positioned to the rear. It is possible that, in this way, the standing position of humans contributed to the evolution of human intelligence. When man started to walk upright, this caused the fetus to lie with the head downwards, so that the brain became more developed. Only when the fetus leaves the womb, the rest of the body starts to overtake the head in growth, and eventually, most of the body's weight is in the lower half. Another similar hypothesis posits that, as the human adopted a standing position, the brain needed to increase its formation of blood vessels, which would be correlated to increased intelligence.
Another animal which spends much of its time in a standing position is the meerkat, which is known for its intelligence and even possesses a primitive language.
Once the embryo knows which side is up and which is down, it can soon tell which way is inside and which is outside: the inside is the the side which receives the embryo's own signaling molecules. The outside is the side which receives the mother's signaling molecules. As the embryo forms a gastrula, the extremities of the embryo nearly touch. Where they touch, there is a high level of interaction which tells the embryo exactly where to place what organs.
At the innermost side of the extremities, the arms and legs will form. At the outermost side of the lower extremity, the head will form, and at the outermost side of the lower extremity, the genitals will form. It might seem paradoxical that the genitals form on the outermost extremity, and not on the innermost side, but keep in mind that at this stage, the embryo will grow in fetus position. Later, as the baby stands, the genitals will appear in front. Even in a fetal photograph this is hard to tell, however, because of the glutes, the muscles of the buttocks, which make legs appear more posterior than they really are: the leg really begins at the acetabulum. It might be more intuitive if one considers that the embryo starts out as female, and that, in addition, it starts out as being similar to other animals.
Yet, the question remains how so many different body parts can form from the same genome. However, our body parts might not actually all be as different from one another as they seem.
We can observe symmetry throughout our bodies, but it could be that there is far more symmetry in our bodies than there seems. Sometimes obvious, sometimes subtle.

Most body parts have a symmetrical twin, that is, there is either an identical or very similar organ on the other half of the body. Symmetrical twins include the arms and legs, the lungs, the brains, the muscles, the kidneys, the ovaries/testicles, the eyes, and so forth. The body partly uses the same DNA for these organs, even if there are differences: for instance, the right and left brain halves have different cytoarchitectures, and the left lung is different than the right lung.
There is no reason for the genome to use two times nearly the same DNA for each of these lungs, and neither would this be possible, for in this case the lungs would have to evolve separately, which would dramatically reduce the change that it would happen at all: it is unlikely enough for a positive mutation to happen. For the same positive mutation to happen two times in the same generation is practically impossible. The same counts for the brain halves, no matter how differently they might work. It is obvious that the genome uses the same DNA for the base of these organs and then uses separate DNA for their differences.
I theorize, however, that symmetrical twins are not the only form of symmetry to be found in the body. We have already seen relatively great differences between obviously symmetrical organs, such as those between the brain halves. Perhaps there are symmetrical organs with even greater differences, differences that are so dramatic that the symmetry between them can no longer be discerned — that is, unless one is looking for them.
For instance, such symmetries can be observed in the digestive tract. This is most apparent in the intestines, especially in the colon, which lies around the small intestine in a symmetrical "M" form. It seems that the colon was originally connected to the rectum at the site of the appendix, as it is at the side of the sigmoid, but, as this made the colon useless, the ascending colon became detached from the rectum.
It is generally believed that only positive mutations are passed on to next generations, while negative mutations are soon eliminated from the species. However, if a mutation is only mildly negative, it may still have a chance of being passed on for long enough for the mutation to come to its use through another mutation, in combination with which it becomes positive. It appears that the colon arose in this way.
The small intestine is basically a more or less symmetrical mass. The stomach seems to be a larger version of the duodenum, and the combination of the two forms a symmetrical S. In fact, the digestive system was originally nothing more than a single (symmetrical!) tube, which in lower organisms such as earthworms, is still the case.
Because higher organisms require so much more energy and therefore nutrients, however, this no longer sufficed, and so the intestine had to curve so as to become long enough to filter enough nutrients. Apparently, the intestines curve in a series of S's. The first S is that of the esophagus from the mouth into the stomach, which is more obvious in fetus position. The second S is that of the stomach and duodenum, and after this, the S's succeed one another rapidly up till the cecum. The acceleration of this succession of S's suggests that, like many systems in our body, it uses the Fibonacci series: in this case, the ratio of the length of each S seems to approximate the ratio of the numbers from the Fibonacci series.
The spleen appears to be the symmetrical analogy of the liver: both filter the blood, both degrade red blood cells, and, in the fetus, both produce red blood cells for some time. Both are contiguous to the digestive system. The liver is larger than the spleen, and the duodenum is proportionally smaller than the stomach.
The galbladder seems to be the symmetrical analogy of the fundus, the uppermost part of the stomach, which has apparently split up from the duodenum.
The pancreas appears to be a symmetrical analogy of the thymus, both of which are endocrine glands. The pancreas is roughly at the same distance from the diaphragm as the thymus. The pancreas lies above the aorta while the thymus lies above the heart, which is basically a mutated section of the aorta. The esophagus lies behind the heart whereas the duodenum lies above both the aorta and the pancreas, but because of how it curves, it was possible that it has twisted its way from behind the aorta to its position before the pancreas. In this way, the pancreas was able to connect with the digestive tract, so that, in addition to being an endocrine gland, it could also become an exocrine gland.
Originally, this connection was an abnormal, congenital fistula, although the fistula did not fully penetrate into the medulla of the pancreas and so the pancreas remained functional. Later, the Brunner's glands in the duodenum at the locus of this fistula mutated and became overgrown, a mutation favored by the fusion of blood vessels with those of the pancreas.
The most obvious symmetry in our body is between the left and right halves of our body, but to a lesser extent, there is also symmetry between the upper and lower halves of our body. For instance, our legs are analogous to our arms. In octopuses, which are some of the most ancient marine animals, this symmetry is particularly striking. Perhaps our entire body is symmetrical not only between the left and right halves, but also between the upper and lower halves.
We have already discussed this symmetry in the intestines, as well as in the pancreas and thymus. Another possible analogous symmetry may be that between the kidneys and lungs. It may seem far-fetched, but if one looks closely, significant similarities can be found between the two, both in structure and function.
As regards function, the lungs collect oxygen-poor blood rich in carbon dioxide and take the carbon from the blood while filling it with oxygen, while the kidneys collect oxygen-rich blood rich in waste compounds and take the waste compounds from the blood while filling it with carbon dioxide.
As regards structure, the pelvis of the kidneys are similar to the bronchia of the lungs, and both are connected to the outside of the body. Even the microscopic structure of the organs are similar: the Bowman's capsules are similar to the alveoli, the main difference being that the glomerulus is inside the glomerular capsule, whereas the alveolar arterioles are outside the alveoli. The collecting tubes are similar to the bronchioli. Furthermore, the lungs and kidneys are the only organs in the abdomen that occur in pairs.
The adrenal glands are likely to have split up from the pancreas as the kidneys shrank in relative size. The ureters are analogous to the bronchia, the bladder analogous to the pharynx.
The face and genitals are the most innervated places on the body, in particular the lips and glandes, but that is apparently as far as any obvious analogies go between the head and hips. This does not mean that there are no other analogies at all, but that they are very ancient. The more subtle the symmetrical analogy, the more ancient it is.
However, the pelvis is possibly analogous to the scapulae and cranium. In early embryonic stages, the cranium is fused to the scapulae, and the scapulae are similar to the ilia of the hips. The ischium, meanwhile, shows similarities to some of the facial bones. The sacrum, which consists of fused vertebrae, may be analogous to the neck, and the coccyx may be analogous to some of the cranial bones. In that case, the ischium would originally be connected to the coccyx in the embryo, and the bones in the hip would form a bowl, as would the bones of the skull and shoulder blades.
Proof of these symmetrical analogies could be found in developing embryos based on Haeckel's principle: the embryo goes through the same development as the species has in the past. If the body really uses these symmetrical analogies in differentiation, it should be observable during differentiation itself.

A bit hypothetical: in a system of points, the average distance from one point to its nearest neighbour is equal to the third root of 6 by the point density:

r = ∛(6/n)


Average Minimal Distance.rtf

A simple formula in combinatorics: for a combination (n,2) (the number of possible pairs formed by n):

(n,2) = Tn - n

where Tn is the triangle number (eg T5 = 5 + 4 + 3 + 2 + 1 = 15). Proof in file.

(n,2).rtf

For people interested in combinatorics…

An excerpt from Tempest - The Transition (http://www.lulu.com/content/1929564)

And Function.rtf

If either the age, size, energy or complexity of the universe are infinite, so are the others: if the universe is infinite in age, it must be infinite in size because a finite universe would keep expanding, ergo in energy, because it would otherwise be of infinitely low density due to this expansion, ergo in complexity because this energy would be distributed amongst the universe rather than remaining infinitely accumulated.
If the universe is infinite in size, it must be infinite in age because if it had a starting point it would originate from a singularity rather than popping into existence in infinite dimensions, and infinite in energy and complexity because it would otherwise be of infinitely low density as formerly said.
If the universe is infinite in energy, it must be infinite in age because in order to become of finite density it'd otherwise have to expand with infinite speed (this is the most plausible other possibility, as the absolute speed of light might not be absolute), infinite in size for the same reason, and infinite in complexity because of its infinite size.
Infinite complexity basically equals infinite size because size is relative. If the universe is infinite up or down, it makes little difference. Suppose the universe was contained inside a giant atom (which would have an infinitely complex substructure, so that this would be possible!), we'd still say the universe is tens of billions of light years in diameter instead of one and a half femtometer. Relative to an infinitely small world (at an infinitely complex level), everything is infinitely large. As we've said, infinite size and finite density means infinite energy. However, if the universe is infinite in complexity this does not necessarily mean that it is infinite in age.

Thus, we conclude that either:
1) the age, size, energy and complexity of the universe are all infinite,
2) neither the age, size, energy or complexity of the universe are infinite
3) the size, energy and complexity, but not the age, of the universe are infinite, and the Theory of Relativity is incomplete.

You can scratch the latter two possibilities, however, if you can accept the following argument. Existence cannot have had an actual cause, because that cause would itself have to be part of existence, otherwise it could not have existed because it would then not be part of existence. Why would there be a beginning? Where did it come from? What caused it? Now, I'm talking about the whole of existence, not just our own reality, but any reality at all, including hypothetical realities in which our own universe was created. Unless there already existed "something" which had caused the universe to arise, ie there was already something in *existence* (in other words, in the universe), such cause would necessarily have been acausal, and for something to be science it must obey causality. Causality, then, is its own only exception. Everything has a cause, but the chain of causes and consequences itself hasn't.

Following this line of reasoning we conclude that the universe is infinite in age, size, energy and complexity. This also implies a universe of infinite complexity. In such a universe, there would be an infinite number of phenomena; each of these would in some way have to influence each other, as they would otherwise not form one whole. Whatever phenomenon would not influence the rest of the Universe would not really be part of it, and therefore not really exist as far as we are concerned. In this way, all phenomena would be infinitely connected to one another, that is to say, each phenomenon would be influenced, directly or indirectly, by infinitely many others. One of such phenomena is our own will, or consciousness, which would likewise be causally interlinked to all other phenomena, meaning that it as well could influence and therefore control them. Thus, in principle, if one would find one's way through this web of causal connections, one could, in principle, control any phenomenon in the universe, meaning that one could be omnipotent. This appears to follow logically if the universe is of infinite complexity.

Something you should surely have read if you've visited my blog at all - probably my most shocking idea.

In an infinite universe, everything is real. Probabilities depend on time and space, thus is both time and space are infinite, all probabilities in the universe are equal to one. This is the basic idea of ergodicity.
This infinity has highly bizarre consequences. Think of the most absurd things you can think of - monkeys raining from a clear sky, trees sprouting from nuclear waste in seconds, atoms arranging themselves to a microscopic epic, molecules across a solar system falling into place to form a hi-tech civilization, a live alien popping into existence in space -- these are all configurations of energy which are theoretically possible, and as Feynman said, anything which can happen will happen. It's all happening, right now and every moment, an infinite number of times. How surreal!
The punchline: the very fact that you can think of something happening means that it IS happening. This principle is known as modal realism: all imaginary worlds are as real as our own, "real" world. Remember that when you're reading a book, or slip into a reverie -- you're having a vision of something which is actually happening.
But it's not over yet -- there's something even more amazing about modal realism…
If everything is real, that means everything is true. After all, it would mean that there is a causal association between all things, and in fact all things are connected. This would actually make all delusions true, as anything that would happen would not only have several causes, but all causes one could think of. For instance, if a paper one looks at suddenly floats away, this would be both because the wind blew it away and because one has telekinetic abilities. There obviously appears to be something wrong here.
In principle, according to chaos theory it may actually be possible to cause a paper to float away by looking at it. But this is not necessarily so, and moreover, it can not be caused both by one's thoughts and the wind.
But because of the ergodic nature of an infinite universe, there would simultaneously be a world where it is caused by the wind and a world where it is caused by one's thoughts, quite simply because if the universe is infinite, everything is. These worlds could otherwise be identical, except in the cause of the paper floating away. Because the universes would be perceived in the same way, they would per definition have the same essence, so that there would be no telling in which of these universes one is. In fact, one could well say one is in both universes at once.
As long as you don't know if something is true or false, it is both true and false, because your own perception matches both the universe where it is true and the universe where it is false. Of course, the only condition for something to be true is that you perceive it to be, that is, that your qualia makes it a possibility (for instance, that you discern something is either true or false, not both). Then, there is always a chance that you'll be in the universe where it is true.
Of course, this chance may be very low, as only in a small percentage of the universes which the many identical "yous" would perceive as identical, it would really be true. Still, however, as long as you have no definitive "proof" whether it is or isn't, it is true, because you have all the perceptions of the you who lives in the universe where it is true, and therefore you are essentially that you. To clarify, nothing really exists if it can't be perceived, thus if the difference between the universe where the idea in question is true and the universe where it is false cannot be perceived, it does not really exist as such, either.
And of course, things are even further complicated because the so-called "proof" that it is or isn't true, which would necessarily be part of one's sensorial input, could be hallucinatory, it'd be essentially worthless: you could still be in a universe where the sensorial input of the proof is an illusion and the idea in question is still either true or false. There is no separation between what we know and what we imagine.
This means that everything is in a dual state, from quantum to universe. This explains the principle of Heisenberg, because we can't (yet) know the state of an individual quantum. This version of this principle is known as the many worlds principle, though the latter was perhaps not founded upon modal realism.
Any possibility one can conceive has a 100% probability of happening somewhere in the multiverse. Thus, any story you can think of is true. Somewhere in the infinite numbers of universes in the multiverse, it happens just like you imagined. If the universe is infinite, space and time are all that separate us from that which we imagine. Imagination, therefore, is a discovery.