Human beings often confound, confuse, and mislead themselves by assuming naively that, in order to be true, a law, principle, or theory must be universally valid without any exceptions. Even in physics, the most successful of all the sciences, there have been examples of valid laws and theories which were later found to be not as universal in their applicability as was formerly believed. One of the most prominent examples is the fact that, although Newtonian mechanics provides a very precise description of the motions of large objects, meaning those that are visible to the naked eye, it has no validity at the atomic and subatomic scales, where other forces besides gravity take precedence, namely the electromagnetic force and the strong and the weak nuclear forces.
In the eighteenth and nineteenth centuries, it was believed that light required a medium to propagate itself through space. This belief arose from the analogy with other kinds of waves that exist on Earth, such as sound waves, which require a physical medium like air or water in order to propagate themselves. This means, for instance, that sound cannot be transmitted through a vacuum. In this case, we can see the erroneous reasoning of those who believed in this light-propagating substance, which they called the ether: all waves, such as sound and water waves, require a medium to propagate themselves; light is a wave; therefore, light also requires a medium to propagate itself through the vast reaches of outer space, such as from the distant Sun or stars to reach the Earth. There were some astonishing qualities that were attributed to this ether, which “was assumed to be weightless, transparent, frictionless, undetectable chemically or physically, and literally permeating all matter and space.” Of course, we now know that the hypothesized ether does not exist, and that not all waves are identical in their properties and requirements for propagation.
There is presently a similar belief that has captivated the scientific community, in particular astronomers, and entered the popular imagination. I am referring to the presumed existence of something called “dark matter.” This dark matter, which is believed to be undetectable by any form of device that can detect or measure radiation, whether visible, infrared, ultraviolet, radio, gamma, x-ray, and so on, is assumed to exist because the calculations of the masses of very large celestial “objects” like galaxies and galaxy clusters, which consist of very large numbers of stars, usually many millions or billions of them, have produced significant discrepancies between the mass that is calculated based on astronomical observations of the total number of stars contained in each galaxy based on their luminosity, or the total number of galaxies contained in a cluster of galaxies, and the mass that is required to hold these massive spinning objects together, as well as the speeds of stars or galaxies in different parts of the galaxy or galaxy cluster.
These calculations are based on the assumption that Newton’s Law of Gravitation is valid at such large astronomical scales. We should remember the important fact that this law was formulated based solely on the study of the objects that exist in our solar system: the Sun, its satellites, or planets, as well as the satellites of these planets, other smaller objects that encircle the Sun, such as meteors, asteroids, and comets, and the objects that lie on or near the Earth’s surface. It was then simply assumed that this law is also valid at all scales of the Universe, including vastly larger scales such as galaxies and galaxy clusters. However, just as it was found that Newton’s Law of Gravitation is not valid at much smaller atomic and subatomic scales, it is also possible that it may not be valid at much larger scales.
There is a rough correlation between the two situations: in terms of scale, as atomic and subatomic distances are to our solar system, the solar system is to galaxies and clusters of galaxies. When it was first understood that atoms are composed of smaller particles, the early model of the atom was based on the solar system, with the electrons revolving around the nucleus, just as the planets revolve around the Sun. Of course, this model of the atom’s structure was later modified because of quantum mechanics. However, just as atoms are believed to consist of tiny particles with a great deal of empty space around them, galaxies and galaxy clusters also consist of small particles of matter – primarily stars, former stars, and planets – with a great deal of empty space that separates them from each other. Hence, it is possible that, just as in the case of atoms and subatomic particles, the force of gravity is not detectable because, at these microscopic distances, other forces are much stronger than gravity, there may exist a relatively weak force that holds galaxies and galaxy clusters together but is not detectable at the much smaller distances of our solar system, where the effects of gravity predominate. In other words, there may indeed be something that is undetectable, but rather than being a vast quantity of missing mass – the hypothetical “dark matter” – it may instead be a force that is not detectable at the distances of our planet and solar system.
If we go back in time to when Newton formulated his famous laws of motion, and in particular his Law of Gravitation, we must remember several things: first, Newton had no idea of how large the Universe actually is, along with how tiny a part of it our solar system comprises; and second, he had no data about the motions of stars within galaxies or the motions of galaxies within galaxy clusters. If he had had this data available to him, as astronomers do today, would he have formulated his Law of Gravitation and declared that it was a universally valid law? My opinion is that he would not have done so. After all, Newton was searching for a mathematical relationship that could accurately describe the motions of all celestial objects, and clearly the Law of Gravitation, although it does a very good job of describing the motions of objects at the scale of our solar system, is not able to describe the motions of larger systems like galaxies and galaxy clusters. What this means is that the assumption – for it is nothing more than an assumption – of this law’s universal validity is due to a historical accident, the fact that Newton was not aware of the nature of the motions of galaxies and galaxy clusters, and the fact that their motions cannot be described by the Law of Gravitation.
There is another point to consider in regard to this matter: in applying the Law of Gravitation to very large systems like galaxies and galaxy clusters, when calculating the expected rotational speed of any one part of it, such as a star or galaxy within the galaxy or galaxy cluster, it is assumed that the masses of all the other stars or galaxies can be treated as if they were concentrated at the centre of the galaxy or galaxy cluster. This simplifying assumption is made because the application of Newton’s Law of Gravitation to work out the orbits of even three bodies – the famous three-body problem – is notoriously difficult, and has been shown to be impossible, except in some special cases. Hence, it may be that this simplifying assumption is invalid at large scales like galaxies and galaxy clusters.
What I suggest to astronomers, then, merely as an intellectual exercise, is to forget about Newton’s Law of Gravitation and see if you can find another mathematical formula that can fit the observations of the motions of stars within galaxies and galaxies within galaxy clusters. In making these comments and proposals, I wish to make clear that I am merely making a conjecture in order perhaps to lead the way to an alternative explanation to the hypothesized existence of this completely invisible and undetectable “dark matter.” But considering how often the naive belief in the universality of laws and principles, whether they are scientific or human, has misled humanity in the past, it is possible that this is merely another example of this common and regrettable mistake.
 Encyclopaedia Britannica, “Ether”. CD-ROM version, 2004.
 It would be more accurate to say that we no longer believe in the existence of this ether because of an alternative, generally accepted explanation for how light and other kinds of radiation are transmitted through space. In the words of the same encyclopaedia article, “With the formulation of the special theory of relativity by Albert Einstein in 1905 and its acceptance by scientists generally, the ether hypothesis was abandoned as being unnecessary in terms of Einstein’s assumption that the speed of light, or any electromagnetic wave, is a universal constant.”
 In what sense can a cluster of galaxies be considered an object? Only when viewed from an immensely far distance does a galaxy cluster appear to be an object; however, this is a case where one’s particular perspective may be misleading, by leading one to attribute unity to something that isn’t really a unity.
 Not all galaxies have a whirl-like shape, as our Milky Way Galaxy does. There are a number of other shapes that galaxies can take on, at least when they are observed from a very large distance, as we observe distant galaxies from the Earth.
 I am aware that the large anomaly between the calculated mass of all visible stars and the mass that is needed to keep very large systems such as galaxies and galaxy clusters together is not derived from Newton’s Law of Gravitation but rather from Einstein’s General Theory of Relativity. But as I do not pretend to understand this theory, I prefer to use Newton’s simpler and more easily understood law as a sort of shorthand to represent the other theory. The discrepancies between the predicted results from these two theories are in fact very small in the case of the masses and velocities that are observable within the confines of our solar system. It is only when one is considering very large masses or very high velocities that their predicted results begin to diverge more and more from each other.
Similarly, in The Theory of Imitation, I used the imprecise term “neural pathway” to designate all the many different, complex processes that exist in the human brain. This was because, in presenting this new theory, my aim was not to describe all these complex processes in precise scientific detail, but rather to present to the lay reader the regularities that exist in the way that our brains make us behave. Thus, for me, since I have never studied neurology, apart from reading a few popular books on the subject, the human brain was a sort of mysterious black control box that receives certain inputs – the observation of certain models of behaviour – and produces certain results: the imitation of these models, in the case of admiration, or conformity to these models, in the case of embarrassment, or a refusal or disinclination to imitate them, in the case of contempt and laughter, along with a strong innate desire to make others imitate these models too. In a nutshell, this last statement neatly summarizes the Theory of Imitation.
 It turns out that someone has already done this. Israeli physicist Mordehai Milgrom has proposed a theory called Modified Newtonian Dynamics which, as its name suggests, modifies Newton’s laws to account for the motions of stars within galaxies. However, at the present time his theory has not gained wide acceptance among physicists because it is not able to account for the motions of the even larger entities known as galaxy clusters, which treats individual galaxies as if they behaved like point masses, with all their mass concentrated at their centres.