Axiomas ou leis do movimiento


Todo corpo permanece em seu estado de repouso ou de movimento uniforme em linha reta, a menos que seja obrigado a mudar seu estado por forças impressas nele.


A mudança do movimento é proporcional à força motriz impressa, e se faz segundo a linha reta pela qual se imprime essa força.


A uma açâo sempre se opôe uma reaçâo igual, ou seja, as açôes de dois corpos um sobre o outro sempre sâo iguais e se dirigem a partes contrárias.

Isaac Newton


On the motion of animals

“Elsewhere we have investigated in detail the movement of animals after their various kinds, the differences between them, and the reasons for their particular characters (for some animals fly, some swim, some walk, others move in various other ways); there remains an investigation of the common ground of any sort of animal movement whatsoever.

Now we have already determined (when we were discussing whether eternal motion exists or not, and its definition, if it does exist) that the origin of all other motions is that which moves itself, and that the origin of this is the immovable, and that the prime mover must of necessity be immovable.

Now in the animal world there must be not only an immovable without, but also within those things which move in place, and initiate their own movement. For one part of an animal must be moved, and another be at rest, and against this the part which is moved will support itself and be moved; for example, if it move one of its parts; for one part, as it were, supports itself against another part at rest.

For all things without life are moved by something other, and the origin of all things so moved are things which move themselves.

And out of these we have spoken about animals (for they must all have in themselves that which is at rest, and without them that against which they are supported); but whether there is some higher and prime mover is not clear, and an origin of that kind involves a different discussion. Animals at any rate which move themselves are all moved supporting themselves on what is outside them (…).

And since all inorganic things are moved by some other thing – and the manner of the movement of the first and eternally moved, and how the first mover moves it, has been determined before in our Metaphysics, it remains to inquire how the soul moves the body, and what is the origin of movement in a living creature. For, if we except the movement of the universe, things with life are the causes of the movement of all else, that is of all that are not moved by one another by mutual impact. And so all their motions have a term or limit, inasmuch as the movements of things with life have such. For all living things both move and are moved with some object, so that this is the term of all their movement, the end, that is, in view. Now we see that the living creature is moved by intellect, imagination, purpose, wish, and appetite. And all these are reducible to mind and desire.

The prime mover then moves, itself being unmoved, whereas desire and its faculty are moved and so move. But it is not necessary for the last in the chain of things moved to move something else; wherefore it is plainly reasonable that motion in place should be the last of what happens in the region of things happening, since the living creature is moved and goes forward by reason of desire or purpose, when some alteration has been set going on the occasion of sensation or imagination.

But how is it that thought (viz. sense, imagination, and thought proper) is sometimes followed by action, sometimes not; sometimes by movement, sometimes not? What happens seems parallel to the case of thinking and inferring about the immovable objects of science. There the end is the truth seen (for, when one conceives the two premisses, one at once conceives and comprehends the conclusion), but here the two premisses result in a conclusion which is an action.

What I need I ought to make, I need a coat: I make a coat. And the conclusion I must make a coat is an action.”


Vehicles: Experiments in Synthetic Psychology

“At this point we are ready to make a fundamental discovery. We have gathered evidence for what I would like to call the “law of uphill analysis and downhill invention.” What I mean is this. It is pleasurable and easy to create little machines that do certain tricks. It is also quite easy to observe the full repertoire of behavior of these machines -even if it goes beyond what we had originally planned, as it often does. But it is much more difficult to start from the outside and to try to guess internal structure just from the observation of behavior. It is actually impossible in theory to determine exactly what the hidden mechanism is without opening the box, since there are always many different mechanisms with identical behavior. Quite apart from this, analysis is more difficult than invention in the sense in which, generally, induction takes more time to perform than deduction: in induction one has to search for the way, whereas in deduction one follows a straightforward path.

A psychological consequence of this is the following: when we analyze a mechanism, we tend to overestimate its complexity. In the uphill process of analysis, a given degree of complexity offers more resistance to the workings of our mind than it would if we encountered it downhill, in the process of invention.”

Valentino Braitenberg

A Foray into the Worlds of Animals and Humans

“Whoever wants to hold on to the conviction that all living things are only machines should abandon all hope of glimpsing their environments.

Whoever is not yet an adherent of the machine theory of living beings might, however, consider the following. All our utensils and machines are no more than aids for human beings. Of course there are aids to producing effects, which one calls tools, a class to which all large machines belong (…). But there are also aids to perception (…). Animals are made thereby into pure objects. In so doing, one forgets that one has from the outset suppressed the principal factor, namely the subject who uses these aids, who affects and perceives with them. (…) One has also gone so far as to mechanize human beings.

For the physiologist, every living thing is an object that is located in his human world. He investigates the organs of living things and the way they work together just as a technician would examine an unfamiliar machine. The biologist, on the other hand, takes into account that each and every living thing is a subject that lives in its own world, of which it is the center. It cannot, therefore, be compared to a machine, only to the machine operator who guides the machine. We ask a simple question: Is the tick a machine or a machine operator? Is it a mere object or a subject?

(…) This is no doubt a case of reflexes, each of which is replaced by the next and which are activated by objectively identifiable physical and chemical effects. But whoever is satisfied with that observation, and assumes he has therefore solved the problem, only proves that he has not seen the real problem at all. (…) It is only a question that, among the hundreds of effects that emanate from the mammal’s body, only three become feature carriers for the tick. Why these three and no others?”

Jakob von Uexküll

Science and The Modern World

“… a general danger inherent in modern science. Its methodological procedure is exclusive and intolerant, and rightly so. It fixes attention on a definite group of abstractions, neglects everything else, and elicits every scrap of information and theory which is relevant to what it has retained. This method is triumphant, provided that the abstractions are judicious. But, however triumphant, the triumph is within limits. The neglect of these limits leads to disastrous oversights… true rationalism must always transcend itself by recurrence to the concrete in search of inspiration.”

Alfred North Whitehead

Dynamics and Self-Organization

“The third problem  [the two first ones being (i) infinite-dimensional space and (ii) preparation of a system in an arbitrary state] seems potentially more tractable, although not yet solved. This is the problem of observation. Indeed, we may distinguish two problems of observation: ignorance and error. By “ignorance” I mean that we look at an infinite-dimensional state, but record only a small number of parameters. Even if we measure without error, the data describe only a point in a finite-dimensional space. Thus, the observation procedure, at best, defines a projection map from the infinite-dimensional state space, S, to a record space, R, of finite dimension. I shall refer to this as the output projection map.”

Ralph H. Abraham

Physiological Optics

“The natural philosopher must stick to the facts and try to find our their laws; and he has no means of deciding between these two kinds of speculation, because materialism, it should be remembered, is just as much a metaphysical speculation or hypothesis as idealism, and therefore has no right to decide about the matters of fact in natural philosophy except on a basis of fact. It is safer in my opinion to connect the phenomena of vision with other processes that are certainly present and actually effective, although they may require further explanation themselves, instead of trying to base these phenomena on perfectly unknown hypotheses as to the mechanisms of the nervous system and the properties of nervous tissue, which have been invented for the purpose and have no analogy of any sort. The only justification I can see for proceeding in this way would be after all attempts had failed to explain the phenomena by known facts. But, in my judgment this is not the case at all with the physiological explanation of visual perception. On the contrary, the more attentively I have studied these phenomena, the more have I been impressed by the uniformity and harmony everywhere of the interplay of the psychic processes, and the more consistent and coherent this whole region of phenomena has appeared to me.”

Hermann von Helmholtz

The Nature of Explanation

“… owing to the Principle of Uncertainty. This lack of verifiability is an unfortunate fact but still does not justify, in my opinion, the confusion between a limit of observation and a limitation of experience. I am not asking physicists to make unverifiable hypotheses as to the nature of the electron (…); I am only asking them to refrain from saying that reality must have the same limitations as their methods of observation. Science surely is an attempt to find our the nature of reality by experiment, theoretical formulation of hypotheses, and verification; not an attempt to assert that reality has the same limitations as our methods of observation. This last is a kind of subjectivism into which science has fallen though it started out to be most objectivist, refusing to accept anything that was not verifiable. It is verifiability which is the fatal link. If a phenomenon is verifiable, it exists; but this does not mean that if it is not verifiable it does not exist. This is the old fallacy: ‘All S are P, therefore all P are S’. The verifiability of statistical predictions shows that the statistical laws are true -that actual objects do behave according to these laws; but it certainly does not prove that these are the ultimate laws which they obey and that there may not be more ultimate mechanisms. Science is not reality; it is a method of investigating reality. (…)”

Kenneth Craik

Mind & Cosmos

“The aim of this book is to argue that the mind-body problem is not just a local problem, having to do with the relation between mind, brain, and behavior in living animal organisms, but that it invades our understanding of the entire cosmos and its history. The physical sciences and evolutionary biology cannot be kept insulated from it, and I believe a true appreciation of the difficulty of the problem must eventually change our conception of the place of the physical sciences in describing the natural order.

One of the legitimate tasks of philosophy is to investigate the limits of even the best developed and most successful forms of contemporary scientific knowledge. It may be frustrating to acknowledge, but we are simply at the point in the history of human thought at which we find ourselves, and our successors will make discoveries and develop forms of understanding of which we have not dreamt. Human are addicted to hope for a final reckoning, but intellectual humility requires that we resist the temptation to assume that tools of the kind we now have are in principle sufficient to understand the universe as a whole. Pointing out their limits is a philosophical task, whoever engages in it, rather than part of the internal pursuit of science (…). Scientists are well aware of how much they don’t know, but this is a different kind of problem – not just of acknowledging the limits of what is actually understood but of trying to recognise what can and cannot in principle be understood by certain existing methods.

(…) For all I know, most practicing scientists may have no opinion about the overaching cosmological questions to which this materialist reductionism provides an answer. Their detailed research and substantive finding do not in general depend on or imply either that or any other answer to such questions. But among the scientists and philosophers who do express views about the natural order as a whole, reductive materialism is widely assumed to be the only serious possibility.

The starting point for the argument is the failure of psychophysical reductionism, a position in the philosophy of mind that is largely motivated by the hope of showing how the physical sciences could in principle provide a theory of everything. If that hope is unrealisable, the question arises whether…”

Thomas Nagel


“Some things benefit from shocks; they thrive and grow when exposed to volatility, randomness, disorder, and stressors and love adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the phenomenon, there is no word for the exact opposite of fragile. Let us call it antifragile.

Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better. This property is behind everything that has changed with time: evolution, culture, ideas,revolutions, political systems, technological innovation, cultural and economic success, corporate survival, good recipes (say, chicken soup or steak tartare with a drop of cognac), the rise of cities, cultures, legal systems, equatorial forests, bacterial resistance … even our own existence as a species on this planet. And antifragility determines the boundary between what is living and organic (or complex), say, the human body, and what is inert, say, a physical object like the stapler on your desk.

The antifragile loves randomness and uncertainty, which also means — crucially — a love of errors, a certain class of errors. Antifragility has a singular property of allowing us to deal with the unknown, to do things without understanding them — and do them well. Let me be more aggressive: we are largely better at doing than we are at thinking, thanks to antifragility. I’d rather be dumb and antifragile than extremely smart and fragile, any time.”

Nassim Nicholas Taleb