But are we clear just what a machine is? Suppose we accept that any piece of nature "is a machine", or that it can, in theory, be analyzed as a machine.
First of all, the everyday usage of "machine" implies a certain class of man made object. How would we describe that class?
The (or one) prevalent modern scientific point of view is to surmise that ultimately underlying all the organic, often amorphous complexity of the world we perceive, is a level at which ultra-miniscule machines function predictably. Electrons spinning around nuclei at an exact, measurable speed; light photons traveling always at a particular speed. At the heart of biological processes are DNA molecules whose properties can in theory be exactly deduced from the sequence of molecules of which they consist.
We want to apply this machine analogy to all of nature, yet we are hard put to find anything that really looks like our everyday notion of a machine, except for those man-made objects that everyday language calls machines. To find mechanical behavior ready-to-hand in nature (before books, economic systems, large-scale governments, and factories came into being), we have to start with systems too simple to fit the everyday notion of a machine. A good example is a rock that is thrown. Once set in motion, there is such predictability about the trajectory of the rock that a skilled person can make it strike in a certain place from 100 feet away.
Now in those caveman days, when we used to throw a lot of rocks, and other projectiles, at animals to kill them for food, it was a great mystery what went on between
(1) the moment when I think of hitting "that animal with this rock" and
(2) the moment when the rock leaves my hand in flight towards the animal.
How does the thought lead to the perfect motion of the hand? A total mystery then, about which even today we have only very partial explanations.
But we have long had a very good understanding of the rock's path from the hand to whatever it strikes. This is called the study of trajectories. In the rennaissance, men like da Vinci and Galileo developed mathematical theories for modeling these trajectories, and used these theories to calculate the elevation of a cannon's muzzle that will make the ball land on the target.
The path of the cannonball, as science tells us today, is so simple and predictable because forces have been isolated. We can almost say that the rock's path is determined by (1) its initial velocity and (2) the earth's gravity, and the interplay between these two "inputs" is indeed simple, and reducible to a formula, as Newton showed.
Now the caveman could not work out this theory; nevertheless the mathematically predictable behavior of a compact heavy object in flight (given its velocity and direction at the moment it goes into free flight) made is possible for the right-brain, which deals with spatial relations in a nonverbal way, to determine how to throw a rock in order to hit a target.
When we build a machine, we build something that somehow, because of its polished, precisely straight or precisely round, or otherwise precisely, regularly, fashioned surfaces, and arrangements, is precisely predictable and controllable. Once set in motion, we know which way it will go; or if we want it to go a certain way, we know how to make this happen. Where do we find anything of such regularity in nature?
The rock or cannonball in flight is one such. But being a system that only exists for a second, it is not very satisfactory. There is one great, exciting, example, which is the solar system. A set of bodies in motion, so arranged that all the possible forces that could come into play have been put into a balance, such that only some few properties determine the visible parts of the system's functioning.
Perhaps we should really study the idea of mechanical regularity, how humankind ever discovered such a thing (which may help us understand something about how the idea is construed by people). What sorts of things we can accomplish with this phenomenon called mechanical regularity, and to what extent does it really pervade nature.
Can we find anything in nature that is demonstrably like a machine?
So I'm saying that mechanical regularity is a rare phenomenon in nature. We have to look very hard to find them, and in doing so, we develop a habit of not focusing on the contingent.
Movements of the stars -- the same stars, night after night, pass in succession; except not quite; there is variation, according to season, in the southernmost(?) visible stars. The gradual recognition of regularity of time; learning how to measure time, and what signs indicate that it is time to plant. Probablistic. The challenge of understanding the movements of the planets. Out of contemplation of the stars and planets -- out of our fascination with this phenomenon which is available and visible to anyone anywhere on earth -- and its remarkable regularity, comes the beginning of truly powerful modeling systems for complex moving systems -- Calculus and Newtonian physics. Other aspects of nature that helped point the way to the exact sciences.
Some precursors came from the study of trajectories, and of optics -- these also can be linked to important mathematical understandings. The behavior of pure substances (chemistry).
If our surroundings seem very regular and controllable, as they do (though maybe not if we were to focus our attention differently), in our technological civilization, it is not just because humankind "discovered" the regularities of nature. It is largely because we rearranged the substances of our world into regular, governable, objects.
[Note: The next and final couple of paragraphs are ruminations that haven't gotten very far, and may appear to point in directions that I would disavow after spending more time with them:]
During the Enlightenment, there was a great fascination with the idea of social engineering. But what do we have to do to make people and societies controllable? We make objects controllable by reshaping them; purifying the materials; making things exactly round or exactly straight or exactly flat (as nearly as possible). Maybe an analogous process with human beings is to reduce motivations to one simple one, which, for someone in the right position, can be easy to manipulate; i.e. fear.
At any rate, that is largely the rule that slave owners followed, and the rule used by the largest-scale social engineers of the last two centuries: Napoleon, Hitler, and the leaders of the large Communist nations.
The liberal economists had a different approach. They did not claim discover a method for making a social machine that would perform acrobatics and turn on a dime, but thought there was great virtue in making everything reducable to money (much as a free-flying object is reducable to mass and speed and direction of movement), so that most of our energy is exerted towards solving an optimization problem: some kind of maximization of wealth.