The Limits of Counterinduction?

A paradox is truth standing on its head to attract attention.

-Nicholas Falletta

Destiny is not a matter of chance-- it is a matter of choice. It is not a thing to be waited for-- it is a thing to be achieved.

-William Jennings Bryan

In this last blog post, I discuss a question that seems to oppose the rest of the arguments presented in this blog: does counterinduction have a limit--i.e. are some laws really untouchable?

The short answer is yes, some laws are untouchable.

The long answer is yes, as long as the realm of science exists in the manner that we know of.

To explain this, I turn again to Kaku's Physics of the Impossible, this time to his Class III impossibilities, or "technologies that violate the known laws of physics."

He points out in the Preface that, 

If they do turn out to be possible, they would represent a fundamental shift in our understanding of physics.

A specific example that he provides is the concept of precognition, or the ability to predict the future. Like many other topics discussed in this blog, precognition has been an area especially interesting to everyone.

(This picture shows a common conception of how "psychics" predict the future, using a "crystal ball.")

In my last post, I talked about  how time travel does not necessarily violate the known laws of science, so one might expect precognition to be a mere corollary to that fact. However, this does not appear to be the case.

The law in question is a very intuitive and simple law-- the rule of cause and effect (causality). Kaku explains that:

Effects occur after the cause, not vice versa. All the laws of physics that have been found so far have causality built into them. A violation of causality would signal a major collapse of the foundations of physics.

And precognition would clearly violate this fact-- if we know of the effect before the cause, a giant plethora of contradictions and paradoxes would instantly rise.

Yet, there are different physical concepts which have tried to counterinductively refute the "impossibility."

One example is embedded in Maxwell's equations for light. When we solve them, we find two solutions: a "retarded" wave that represents the standard movement of light, and an "advanced" light that actually goes backward in time.

HUH?

Yes, light that travels backward in time. It probably confused you, it confused me, and it definitely confused mathematicians and physicists.

But surely, if light and electrons have the ability to travel to the past already, then we can send messages through them, right? Doesn't this fact show the violation of causality?

The answer is no.

This is because as the electron travels to the past, it simply fulfills the past. No violations of causality are made, and none can be made if we treat antimatter as just another form of matter. In fact, antimatter is essential to restoring causality!

Hence, Kaku concludes that,

Precognition seems to be ruled out, at least for the foreseeable future...It would set off a major shake-up in the very foundations of modern physics if precognition was ever proved in reproducible experiments.

Hence, we can conclude that although counterinduction is a powerful tool, it still has its limits, at least in our foundations of science.


This concludes the discussion of Feyerabend's Against Method and Kaku's Physics of the Impossible.

Impossible Now, Possible in the Future

"If time travel is possible, then where are the tourists from the future?"

-Stephen Hawking

"[Time travel] is against reason," said Filby.

"What reason?" said the Time Traveler

-H. G. Wells

Kaku's second group of impossibilities-- Class II impossibilities-- are "technologies that sit at the very edge of our understanding of the physical world. If they are possible at all, they might be realized on a scale of millennia to millions of years in the future." An example that will be discussed here is the idea of time travel.

Like invisibility, time travel has been discussed by everyone-- from scientists and philosophers to innocent children, all throughout the ages. Yet most have so far assumed that such ideas of traveling to the past or to the future is an impossible task, as that would bring out numerous well-known paradoxes. (Tor example, if you go to the past and prevent your parents from meeting, will you exist?) 

And for a while in scientific history, the impossibility of time travel was supported by physics: in Newton's universe, time was labeled as being absolute-- a second on earth was thought to be a second in the entire universe. Time would be an unstoppable arrow.

This all changed with Einstein's new, revolutionary developments in physics, in which he showed that time is like a river, speeding up and slowing down as it flows throughout the universe. In his special theory of relativity, he explained how in a rocket, for example, time slows down the faster it moves. As it approaches the speed of light, time slows down.

Thus, the idea of time travel being impossible was broken: now, we know that time travel is possible (albeit not as nearly as close to the level that we imagine). In fact, the world record for traveling into the future is held by Russian cosmonaut Sergei Avdeyev, who was hurled 0.02 seconds into the future.

Yet even this picture may not be complete! In Einstein's perspective, time travel to the past would still be impossible, as an object would have to travel faster than the speed of light to accomplish such a journey. For instance, in Superman I Superman tries to go back in time by circling around the Earth faster than the speed of light:

(The scene from Superman: The Movie)

However, in order for this to happen, an object would have to have an infinite mass! Yet new discoveries are already suggesting that the speed of light barrier has been broken: researchers at CERN have possibly found that neutrinos (which certainly do not have infinite mass) can travel faster than the speed of light! 

This further reveals just how a standard approach to science only hinders scientific achievement. Had we fully taken Einstein's ideas of science to heart, such discoveries would have never been made, and the scientific community would have been covered in a veil of ignorance. A pluralistic and counterinductive approach, on the other hand, would ensure that (at least) attempts are made to directly challenge such "well-established" theories.

(Referring to the paradox mentioned above, Kaku offers three possible answers/hypotheses:

First, perhaps you simply repeat past history when you go back in time, therefore fulfilling the past. In this case, you have no free will. You are forced to complete the past as it was written. Thus, if you go back into the past to give the secret of time travel to your younger self, then it was meant to happen that way. The secret of time travel came from the future. It was destiny. (But this does not tell us where the original idea came from.)

Second, you have free will, so you can change the past, but within limits. Your free will is not allowed to create a time paradox. Whenever you try to kill your parents before you are born, a mysterious force prevents you from pulling the trigger. This position has been advocated by the Russian physicist Igor Novikov. He argues that there is a law preventing us from walking on the ceiling, although we might want to. Hence, there might be a law preventing us from killing our parents before we are born.

Third, the universe splits into two. On one timeline the people whom you killed look just like your parents, but they are different, because you are now in a parallel universe. This latter possibility seems to be the one consistent with the quantum theory.)

Will We See Invisibility in the Future?

"You cannot depend on your eyes when your imagination is out of focus."

-Mark Twain

Kaku separates scientific "impossibilities" into three classes: he describes Class I impossibilities as "technologies that are impossible today but that do not violate the known laws of physics." A primary (and very popular) example is invisibility.

(The idea of invisibility also showed up in Harry Potter. Here, Harry is seen to be wearing an "invisibility cloak," which turns anything it touches invisible.)

From ancient civilizations to current science fiction communities, the idea of invisibility has been very popular and well-known. Yet until just a few years ago, scientists had strongly believed that "metamaterials," which are substances that have unusual properties that have the potential to render objects invisible, cannot physically exist due to the laws of optics.

The process started in 1967, when Soviet physicist Victor Veselago theorized the inconsistent existence of these metamaterials. The ideas and consequences that these brought were so bizarre that they were thought to be impossible to construct.

This all changed in 2006, with groundbreaking research at Duke University and Imperial College.

Scientists there successfully defied conventional "knowledge" by creating an object invisible to microwave radiation. Although we cannot see the direct difference with the naked eye, it was nonetheless a crucial step toward an optical revolution.

Although many scientists initially held onto their theoretical laws of optics, arguing that a negative index of refraction (a number that describes how radiation propagates through a medium) is impossible and that metamaterials must have a negative value, they were reluctantly forced to rewrite all the textbooks on optics.

An even bigger step was taken in early 2007, when scientists in Germany and the U.S. Department of Energy anounced that they had formed metametrials that worked for red light as well as microwave radiation. Such creations foreshadow several drastic changes in optics, as well as the rise of true invisibility.

Kaku thus declares that, "The 'impossible' had been achieved."

It is important here to note how arguing and proposing inconsistent hypotheses-- those which contradicted "established" laws and theories-- were crucial in the making of the metamaterials; for instance, had Veselago not proposed his idea due to pressures by the previously-existing laws of optics, the idea of metamaterials might not have even been discovered now. We must remember that, especially in the realm of such Class I impossibilities, keeping an open and pluralistic mind is the only way to achieve the impossible.

Entering the Realm of the Impossible

Michio Kaku, in his Physics of the Impossible, tackles numerous topics which the general scientific community-- as well as the general public-- views as being impossible to occur. However, is this really the case, or is the idea of impossibility strictly relative? Can we, in fact, teleport to anywhere, build spaceships that can take us light-years away into space, or do any other "crazy" activities that the scientific community takes lightly?

Kaku responds that,

Normally such feats would be considered impossible by today's physicists. Might they become possible within a few centuries? Or in ten thousand years, when our technology is more advanced? Or in a million years? To put it another way, if we were to somehow encounter a civilization a million years more advance than ours, would their everyday technology appear to be "magic" to us?...Just because something is "impossible" today, will it remain impossible centuries or millions of years into the future?

He first mentions Jules Verne's novel Paris in the Twentieth Century, which was written in 1863. In it, he predicts a world clearly considered to be impossible at his time: a world with "fax machines, a world-wide communications network, glass skyscrapers, gas-powered automobiles, and high-speed elevated trains." The same scene, Kaku claims, is happening right now as well, and that we must recognize an analyze it to the best of our abilities.

He also includes historical examples which were considered at some point in time to be impossible, mentioning ideas such as quantum theory and "alchemy" (the idea of changing one element to another) and inventions such as airplanes, X-rays and atomic bombs. Even black holes were once "proved" to not exist by Einstein.

(Notice how even the picture similarly parallels our current world.)

Kaku explains that such failures to predict the "impossible" result from "huge gaps in the understanding of science at the time." He subscribes to T.H. White's quote from his The Once and Future King: "Anything that is not forbidden, is mandatory!" By so, he means that unless a specific scientific law forbids a new phenomenon, it is eventually found.

Similar to Feyerabend's arguments, regarding those banned by fundamental laws Kaku still maintains that,

If they do turn out to be possible, they would represent a fundamental shift in our understanding of physics.

Thus he suggests that they may not be as impregnable as the scientific community believes, and that the impossible may still happen.

With that in mind, we dive into some of the "impossibilities" of today...starting from the next post.

Can Unity Be Bad?

In one of the final chapters of his essay, Feyerabend attacks the conventional notion of the benefits of scientific unity. He outlines three main questions:

1. What is science? How do scientists proceed, how do their standards differ from the standards of other enterprises? 

Unlike other scientists or philosophers of science who try to define science in the most efficient and encompassing ways possible, Feyerabend instead argues that such mechanisms, while they may help analyze the achievements and drawbacks of various approaches, eventually only serve to "put one view on top and subordinate the others to it, either by pseudo-derivations, or by declaring them to be meaningless."

Basically, he declares that by narrowing and bounding science to a single interpretation and a single coherent world-view, we at best try to "anticipate a future unity" and at worst bring about a giant "pedagogical fake." He quotes John Ziman, who in his Teaching and Learning About Science and Society argued that,

There is no simple "scientific" map of reality - or if there were, it would be much too complicated and unwieldy to be grasped or used by anyone. But there are many different maps of reality, from a variety of scientific viewpoints.

 Feyerabend also suggests that by limiting science to one definition we reject the possibility of conflicting or inconsistent hypotheses and theories, which can rise to be crucial in scientific advancements.

2. What's so great about science? What are the reasons that might compel us to prefer the sciences to other forms of life and ways of gathering knowledge?

"Popularity, i.e. familiarity with some results and the belief that they are important," is "a measurement of greatness," as Feyerabend describes. But the flaw lies in the fact that the general public believes in a singular, "mythical monster 'science'." The public assumes that

the achievements they read about in the educational pages of their newspapers and the threats they seem to perceive come from a single source and are produced by a uniform procedure. They know that biology is different from physics which is different from geology. But these disciplines, it is assumed, arise when 'the scientific way' is applied to different topics; the scientific way itself, however, remains the same.

But it must also be noted that the fact that a specific approach is "scientific" by some criterion does not guarantee its success or efficiency; each case, each approach, each methodology must be judged and analyzed separately. By perceiving science as a single approach, we (including the general public) narrow our vision to disregard theories that directly oppose conventional ideas, which serve as the main tool for scientific change.

 3. How are we to use the sciences and who decides the matter?

Regardless of the negative consequences that such appeals to a chimaera bring to the field of science, he still mentions that it can have crucial political impacts:

A uniform 'scientific view of the world' may be used for people doing science - it gives them motivation without tying them down. It is like a flag. Though presenting a single pattern, it makes people do many different things.

 Thus a community will use science in "a way that agrees with its values and aims," and it will also use it to "correct the scientific institutions in its midst to bring them closer to these aims." Politically, such ideas can be a political tool that sparks scientific progress.

Nonetheless, Feyerabend warns that,

It is a natural disaster for outsiders...It suggests to them the most narrowminded religious commitment and encourages a similar narrowmindedness on their part.

*This post concludes the analyses of Feyerabend's Against Method and marks the short beginning of the applications of topics from Michio Kaku's Physics of the Impossible.

Observations Revisted

Stepping out of the book for a second, I wanted to note another author who shared similar beliefs.

Recently I read Norwood R. Hanson's short article called "Observations," in which he depicts a familiar scenario:

Imagine [Johannes Kepler] on a hill watching the dawn. With him is Tycho Brahe. Kepler regarded the sun as fixed: it was the earth that moved. But Tycho followed Ptolemy and Aristotle in this much at least: the eath was fixed and all other celestial bodies moved around it. Do Kepler and Tycho see the same thing in the east at dawn?

He describes a situation in which two people view the same object but consider it to be different. In this case, obviously, Kepler saw the Earth moving while Tycho saw the Sun moving. So one might ask, why do we even need to incorporate all such mindsets, as Feyerabend proposes?

Surprisingly, this example rather highlights the need to compare and contrast between various different theories. When Kepler, Copernicus, Galileo, and other astronomers began to note observations that contradicted the geocentric model, they brought revolutionary changes in the field of astronomy. Yet had such inconsistent data challenged the geocentric model directly, the arrival of the heliocentric model might not have arrived at that point in time. Had such observations not been used, the world would have lived in scientific ignorance for a longer time.

Furthermore, the "established" theory could simply be one of the interpretations of the observations. Because different people view different objects differently, it is definitely possible that the interpretation is subjective and incomplete. This is exacerbated by the fact that most scientists try to prove current or established theories, rather than simply exploring possible scenarios. Such a fixed and short-sighted mindset is the source of such subjectivity, and it will be impossible to break away from that cycle unless alternative observations and theories are considered. Thus a combined analysis is the only way to determine the best theory that can result with given facts.

Thus fittingly, Hanson concludes by saying that,

Sorting out differences about data, evidence, observation, may require more than simply gesturing at observable objects. It may requires a comprehensive reappraisal of one's subject matter. This may be difficult, but it should not obscure the fact that nothing less than this may do."

Is Science Just a Tradition?

In an interesting chapter, Feyerabend describes how scientists now perceive current standards of science as measurements of excellence. He points out and asks,

Modern science arose from global objections against earlier views and rationalism itself, the idea that there are general rules and standards for conducting our affairs, affairs of knowledge included, arose from global objections to common sense...Are we to refrain from engaging in those activities that give rise to science and rationalism in the first place? Are we to rest content with their results? Are we to assume that everything that happened after Newton (or after Hilbert) is perfection? Or shall we admit that modern science may have basic faults and may be in need of global change?

He then moves on to describe the act of choosing a particular field of research not because of its intrinsic "perfection" but because he/she wants to see where it leads, which he labels as the pragmatic philosophy. He claims that such a philosophy can only flourish if

The traditions to be judged and the developments to be influenced are seen as temporary makeshifts and not as lasting constituents of thoughts and actions.

So what is the issue here? The problem lies in the fact that one cannot see his/her own, cherished tradition in perspective, as "parts of a changing and, perhaps, absurd tradition." Such a mindset, Feyerabend claims, is the reason for the illogical process of maintaining one specific "tradition" and disregarding the rest. We preserve these standards, when actually they should be attacked with varying, alternate beliefs.

But how do we never notice these alternative beliefs? Surely, if they are significant enough to make such a difference, then they ought to pop up! Feyerabend, in response, explains how we do notice these different traditions-- in a different form: when critics of a certain practice "discover" flaws and limitations that contradict another set of beliefs, they are merely noticing that the two bodies of ideas-- the one being criticized and the one used in the criticism-- simply do not fit each other.

He provides a simple example:

Many arguments against an out-and-out materialism are of this kind. They notice that materialism changes the use of 'mental' terms, they illustrate the consequences of the change with amusing absurdities (thoughts having weight and the like) and then they stop. The absurdities show that materialism clashes with our usual ways of speaking about minds, they do not show what is better - materialism or these ways. But taking the participants' point of view with respect to common sense turns the absurdities into arguments against materialism.

He jokes that "It is as if Americans were to object to foreign currencies because they cannot be brought into simple relations (1:1 or 1:10 or 1:100) to the dollar.

Rather than seeing the situation as a comparison between two traditions, the participants of a tradition blindly follow theirs as the truly "objective" belief. Thus, when they defend the "objectivity" of such values, they only use their beliefs instead of examining and analyzing it. This does not make the tradition an "objective measure of validity," nor does it show that the specific tradition is any good.

Therefore, in order to break this cycle and critically examine all "standards" and traditions, Feyerabend argues that we must be able to recognize these different traditions instead of using one to reject another.

Criticizing Critical Rationalism?

Karl Popper's concept of critical rationalism held that scientists should continually try to falsify current theories to legitimize them,

Philosopher of science Karl Popper, main proponent of the theory of critical rationalism

To his ideas, Feyerabend asks two questions:

1. Is it desirable to live in accordance with the rules of a critical rationalism?

2. Is it possible to have both a science as we know it and these rules? 

 To the first question, he describes briefly how solely objective and almost-mechanical processes of thinking such as that of critical rationalism slowly detach all freedom and other human interests: as he asks,

Is it not possible that an objective approach that frowns upon personal connections between the entities examined will harm people, turn them into miserable, unfriendly, self-righteous mechanisms without charm and humour?

To understand this specific argument further, Feyerabend suggests Kierkegaard's work Papirer.

 Feyerabend then expands further on the second question at hand, and focuses on the fact that such principles of critical rationalism "give an inadequate account of science because science is much more 'sloppy' and 'irrational' as its methodological image." Moreover, he refers to his previous chapters in which he discusses the fallacies behind the process of falsification-- or the method of rejecting theories based on "inconsistencies" (also see my previous posts about the example with the heliocentric model, of which this is one of).

Furthermore, he also argues how

Theories which [affect] the overthrow of a comprehensive and well-entrenched point of view, and take over after its demise, are initially restricted to a fairly narrow domain of facts, to a series of paradigmatic phenomena which lend them support, and they are only slowly extended to other areas.

In the process of developing a new theory, we must step back and reconsider the problem. At this point, the emerging conceptual apparatus begins to "define its own problems, and earlier problems, facts, and observations are either forgotten or pushed aside as irrelevant." And this outcome, he argues, is especially harmful to scientific advancements by the numerous arguments that he notes in the first few chapters.

Lastly, he mentions at the end of the chapter that,

There is not a single rule that remains under all circumstances and not a single agency to which appeal can always be made.

Does this statement suggest that the notion of critical rationalism is also flawed because every theory can be rejected? Do there exist 'laws" that always work? I leave these questions open for the reader to ponder upon.

Reason vs. Irrationality

The pivotal theme of Feyerabend's essay is the necessity of the preservation of all theories:

We must retain the new cosmology until it has been supplemented by the necessary auxiliary sciences. We must retain it in the face of plain and unambiguous refuting facts.

 As he emphasizes constantly, a new theory which "contradicts" an old idea or system should not be automatically discounted, as

The contradiction only indicates that the old and the new are different and out of phase. It does not show which view is the better one.

This brings up a very important question, which Feyerabend points out in chapter 11:

How can we persuade people to follow our lead? How can we lure them away from a well-defined, sophisticated and empirically successful system and make them transfer their allegiance to an unfinished and absurd hypothesis?

It would make sense that people would be very reluctant to change from the status quo; after all, who wouldn't choose to believe in theories supported logically and empirically? In addition, who would want to replace such beliefs with those that are inconsistent with so many observations?

To this Feyerabend offers a surprising approach:

It is clear that allegiance to the new ideas will have to be brought about by means other than arguments. It will have to be brought about by irrational means such as propaganda, emotion, ad hoc hypotheses, and appeal to prejudices of all kinds. We need these 'irrational means' in order to uphold what is nothing but a blind faith until we have found the auxiliary science, the facts, the arguments that turn the faith into sound 'knowledge.'

 This, undoubtedly, is the only means of achieving the far-fetched goal that Feyerabend dreams of. Yet how can anyone argue that we should follow an approach that follows from irrationality and "blind faiths"? Wouldn't it be better to stick with rationality and reasoning?

To this, Feyerabend responds by saying that,

What our historical examples seem to show is this: there are situations when our most liberal judgments and our most liberal rules would have eliminated a point of view which we regard today as essential for science, and would not have permitted it to prevail - and such situations occur quite frequently.

The main example that he cites refers (again) to the heliocentric model from Copernicus. He regards Copernicus as "a symbol for the ideals of a new class that looks back to the classical times of Plato and Cicero and forward to a free and pluralistic society." Although we currently hold the heliocentric model as a fact, at his time the proposed system was ridiculed. Numerous arguments-- such as the tower argument (which I mentioned a few days ago)-- had caused almost all scientists to reject it. At the time, the geocentric model was "established," with "facts" and "observations" supporting the idea. This example supports Feyerabend's warnings and reveals the possibility of our current beliefs to be erroneous as well.

Furthermore, he mentions how Galileo, another scientist at the time, had used the exact methodology that is mentioned above-- by using "tricks, jokes, and nonsequiturs of his own."

In essence, Feyerabend contends that we must break the cycle of using only (ignorant) reason and maintain the possibility of any alternatives to rise up.Thus he concludes the argument by declaring that,

[These ideas] survived because prejudice, passion, conceit, errors, sheer pigheadedness, in short because all the elements that characterize the context of discovery, opposed the dictates of reason and because these irrational elements were permitted to have their way.

But should we really hold onto such "blind faiths"? Should we support a scientific "method" which relies on deceit and propaganda? And most importantly, are such revolutionary breakthroughs like those from Copernicus and Galileo important enough to replace reason with irrationality?

Facts vs. Observations

Earlier in this blog, I mentioned Feyerabend's idea of being cautious of one's senses. Later on in his essay he offers another grander, historical example:

Again regarding the theory that the Earth moves (a highly controversial hypothesis at the time), he cites Galileo, who praises the "followers of the Pythagorean opinion [that the earth moves]." He specifically refers to those who choose to trust their logic and rationality over the countless observations via senses that oppose the theory of the movement of Earth.

Another observational example, other than the tower argument (mentioned yesterday), that strongly shows otherwise deals with the movement of other planets and is described by Galileo:

Mars, when it is close to us...would ahve to look sixty times as large as when it is most distant. Yet no such difference is to be seen. Rather, when it is in opposition to the sun and close to us it shows itself only four or five times as large as when, at conjunction, it becomes hidden behind the rays of the sun. 

 Furthermore, regarding Copernicus and his revolutionary (no pun intended) ideas for Venus, Galileo states:

I cannot get over my amazement that he was constantly willing to persist in saying that Venus might go around the sun and might be more than six times as far from us at one time as at another, and still look always equal, when it should have appeared forty times large. 

Feyerabend cites these observational arguments to show that such claims only create an illusion that prevents us from discovering the truth, and that rationality must be prioritized in order to escape such illusions.

Yet overcoming one's senses and replacing them with reasoning is no small feat. This explains why Galileo so admires those who "have, through sheer force of intellect, done such violence to their own senses as to prefer what reason told them over that which sensible experience plainly showed them to be the contrary."


*All quotes by Galileo were from his Dialogue Concerning the Two Chief World Systems, and were taken from Feyerabend's essay.

Induction vs. Counterinduction

Counterinduction is a notion that is heavily emphasized in Feyerabend's work. This is the argument opposite of induction: it argues that rather than generalizing one statement that follows empirical examples, one should do the opposite and argue different, inconsistent claims. An example would be "The sun set every day in the past, so it will not set today."

At first, this argument seems completely silly and erroneous; why would anyone want to make a statement that contradicts all empirical "facts" provided? Well, Feyerabend has shown through numerous arguments (some of which are posted on this blog below) how counterinduction can be a more efficient tool for scientific discovery than the usual induction.

He starts on chapter 5 that,

As an example of such an attempt I examine the tower argument which the Aristotelians used to refute the motion of the earth. The argument involves natural interpretations - ideas so closely connected with observations that it needs a special effort to realize their existence and to determine their content.

The "tower argument" asserts that since an object falling from a tower moves vertically and not diagonally, the Earth cannot be moving.

This observational "fact"-- labeled by Feyerabend as a natural interpretation, was believed to be so "obvious" that theories contradicting this idea were quickly rejected.

However, Feyerabend asserts that such observational "facts" must not be taken for granted. Analyzing Galileo's works, he argues that even this "basic" fact assumes a "naive realism with respect to motion." Because relative motion from a point of view on Earth is not separated or distinguished from absolute motion, this empirical example creates a false illusion that the Earth must be moving. The latter concept of motion became a new interpretation of the situation and counterinductively allowed us to realize the flaws associated with the original assumption.

Psychologically, admitting the fact that one did not notice the object moving in such a wide trajectory as seen in the image above can be very difficult-- a situation Feyerabend calls a paradigmatic case. Even in these cases, however, the counterinductive interpretation allowed us to notice the Trojan horse behind the natural interpretation. 

Thus, we cannot stick with one "accepted" theory that encompasses these "known" facts. But we cannot reject all natural interpretations, as without them a person would be "completely disoriented" and would not be able to "start the business of science." So how can we deal with such empirical "facts" and theories?

Feyerabend argues that the only logical option left is to form many theories, with some contradicting others, so that we can counterinductively analyze and determine the validity of these "facts." As he says, we need to use an "external measure of comparison, including new ways of relating concepts and percepts." This strange approach will reveal how such natural interpretations actually work.

In the example above, the Copernican view of the motion of the Earth acts as the "external measuring rod." It allows us to uphold apparent contradictions until we completely examine them, "or else the examination, the attempt to discover the antediluvian components of our knowledge, cannot even start." 

Since a particular natural interpretation cannot be tested directly (by comparing them with former "results of observation"), the use of other interpretations is the only option left. Therefore, Feyerabend declares that,

Ideological ingredients of our knowledge and, more especially, of our observations are discovered with the help of theories which are refuted by them. They are discovered counterinductively.

Facts vs. Theories

Another interesting argument that Feyerabend mentions can be summarized as the following, in his words

No theory ever agrees with all the facts in its domain, yet it is not always the theory that is to blame. Facts are constituted by older ideologies, and a clash between facts and theories may be proof of progress. It is also a first step in our attempt to find the principles implicit in familiar observational notions.

In this segment, he states that because no theory, no matter how well-established or encompassing it is, will fail to be consistent with all facts in its domain. This is the example that he provides:

The perihelion (the point closest to the Sun) of Mercury moves at a rate of roughly 5600" per century. Of this value, roughly 43" are derived from a relativistic calculation; specifically, the so-called "Schwarzschild solution" does not involve the planetary system of this real world, but rather it assumes a fictional, perfectly central and symmetrical universe.

The reason for using such solutions, scientists claim, is that we deal with approximations in science. Yet Feyerabend argues that such ad hoc approximations "conceal, and even eliminate, qualitative difficulties." Although not as apparent in this example, such approximations eventually give a false impression of the "excellence" of our science. Feyerabend relates this methodology to a medicine that "heals a patient only if he is bacteria-free."

He maintains that,

A theory may be inconsistent with the evidence, not because it is incorrect, but because the evidence is contaminated.

When we, for instance, reject theories because they conflict with "data" or "evidence" using approximations with unrealistic scenarios, we do so unfairly. We fail to recognize the validity of new theories because we engrave the "framework of some older cosmology." This is why, he argues, that we need to have a pluralistic mindset, comparing and analyzing all possible theories, especially those that directly go against "accepted" ideas. We must be able to criticize such theories via comparisons, since direct analyses will only hinder efforts.

He thus concludes that,

The right method must not contain any rules that make us choose between theories on the basis of falsification. Rather, its rules must enable us to choose between theories which we have already tests and which are falsified.

Karl Popper, a strong proponent of the falsification methodology, would undoubtedly have a strong response against it.

Does Older=Better?

Another main argument that Feyerabend puts forward can be summarized in his statement:

The consistency condition which demands that new hypotheses agree with accepted theories is unreasonable because it preserves the older theory, and not the better theory. Hypotheses contradicting well-confirmed theories give us evidence that cannot be obtained in any other way. Proliferation of theories is beneficial for science, while uniformity impairs its critical power. Uniformity also endangers the free development of the individual.

In other words, every time we reject theories that are inconsistent with older, more "established" theories, we make logical fallacies known as "appeal to antiquity," which falsely asserts that older theories are better theories.

We can clearly see why we do not want such consequences in science; if Theory B is rejected because Theory A came first, then in a world where Theory B was discovered first Theory A would have been rejected. The validity of a theory is replaced with its age. Although this might be an oversimplification of the issue, the crux of the matter still holds.

A recent example of this deals with the field of crystallography. As I mention in another blog Synthesis of Symmetry, the Crystallographic Restriction Theorem, proven mathematically, states that a periodic solid, which is ordered on a microscopic level, can only have 2-fold, 3-fold, 4-fold or 6-fold rotational symmetries.

(A typical snowflake is seen to have a 6-fold symmetry.)

This Theorem has been established and accepted by scientists everywhere, and has been heralded as a fact. However, Dan Shechtman and his team in 1984 discovered and argued for the existence of quasicrystals (or quasiperiodic crystals) that have rotational symmetries of other degrees. At first his paper and his theory had been rejected by almost the entire scientific community; scientists who had taken the original Theorem to heart had tried to discredit the new, rising theory in every way possible. As Shechtman said, "For a long time it was [him] against the world."

But eventually, Shechtman had been successful in persuading the rest of the scientific community that quasicrystals do exist, and that the Theorem is at least incomplete, and that crystals with other forms of symmetry do exist. (He subsequently received a Nobel Prize for his work in 2011.) Had we not explored the new concept and stuck with the "older is better" mindset, such revolutions in scientific history would never have occurred.

In fact, Feyerabend argues that there are areas in science where pluralistic thinking is necessary for the discovery of facts. He cites the example of Brownian particles, which are perpetual motion machines of the second kind (meaning that they constantly and spontaneously converts thermal energy into kinetic energy). The fact that this violates the second law of thermodynamics cannot be observed directly; he argues that the measurements needed to show it directly are "beyond experimental possibilities" of the status quo. Thus we can see how considering other scenarios and hypotheses-- in this case, for example, an alternative theory of heat-- can be vital in the discovery of facts.

Such anarchistic and pluralistic approaches to science have been historically shown to be fundamental in the search for facts. They are they only ways for us to see just how incomplete are the theories that we "know" of now.

Is That Table Really Brown?

One main argument that Feyerabend mentions can be found in chapter 2 of his essay, where he summarizes that,

We may use hypotheses that contradict well-confirmed theories and/or well-established experimental results. We may advance science by proceeding counterinductively.

He argues that such a standardized methodology of science in the status quo, where theories and hypotheses that contradict current observations, experimental results and other "facts" are discouraged. The example for his justification is very interesting, thought-provoking, and fundamental to science itself:

When we see that a table is brown, we tell ourselves (unsurprisingly) that, "the table is brown." When others come up to us and say, for instance, that the table is purple, we immediately strike the idea down.

And why wouldn't we? After all, we "know" ourselves (unless we are colorblind, of course) that the table is indeed brown. But aren't we assuming something?

As Feyerabend points out, we "take it for granted that the material medium between the object and us exerts no distorting influence, and that the physical entity that establishes the contact - light - carries a true picture." Such abstract assumptions, which many would consider as simply trivial, actually "shape our view of the world without being accessible to a direct criticism."

In fact, unless we are faced with a contrasting cosmology (in this example, the statement that the table is purple), we fail to recognize and resolve the underlying assumptions.

Thus we can agree that "a theory may clash with the evidence not because it is not correct, but because the evidence is contaminated.

Analogously, in a world where hypotheses that contradict "given" observations are rejected, such principles would be impossible to examine. This is why Feyerabend argues for a pluralistic approach of science, so that we can create an environment for clashes with the most established results and the most plausible principles.

The only way to achieve this, of course, is to remove the framework of an organized methodology of science. Only in a scientifically anarchistic nature, where "anything goes," can we be unlimited in our scientific endeavors.