Scientific method

In memory of Paul Feyerabend, who died thirty years ago, on November 11, 1994 

Izumi Miyazaki

My intention is not to replace one set of general rules by another such set: my intention is, rather, to convince the reader that all methodologies, even the most obvious ones, have their limits. The best way to show this is to demonstrate the limits and even the irrationality of some rules which she, or he, is likely to regard as basic. 

Paul Karl Feyerabend

Against Method: Outline of an Anarchistic Theory of Knowledge (1975)

ημιμάθεια

Η παγίδα της ημιμάθειας:

γνωρίζω για κάποιο θέμα τόσα, ώστε να νομίζω ότι έχω δίκιο

αλλά δεν γνωρίζω αρκετά, ώστε να καταλαβαίνω ότι κάνω λάθος

εκείνος που καταλαβαίνει

 

Language and Science

Hieronymus Bosch - Garden of Earthly Delights

Language is a social creation. It encodes the common experience of many people, past and present, and has been sculpted mainly to communicate our everyday needs. Ordinary language is most certainly not a product of the critical investigation of concepts. Yet scientists learn, think and communicate in it during much of their lives. Ordinary language is therefore an unavoidable scientists’ tool — rich and powerful, but also quite imperfect. 

One scientific imperfection of language, perhaps the most obvious, is its incompleteness. For example, there are no common words for several of the most central concepts of quantum theory, such as the linearity of state-space and the use of tensor products to describe composite systems. To be sure, we’ve developed some applicable jargon — ‘superposition’ and ‘entanglement’, respectively, are the words we use — but the words are unusual ones, not likely to convey much to outsiders, and their literal meaning is misleading to boot. 

Although it creates cultural barriers and contributes to the balkanization of knowledge, such enrichment and slight abuse of language is not a serious problem. Much more insidious, and more fundamentally interesting, is the opposite case: when ordinary language is too complete. When something has a name, and the name is commonly employed in discourse, it is seductive to assume that it refers to a coherent concept, and an element of reality. But it need not. And the more pervasive the word, the more difficult it can be to evade its spell. 

Few words are more pervasive than ‘now’. According to his own account, the greatest difficulty Einstein encountered in reaching the special theory of relativity was the necessity to break free from the idea that there is an objective, universal ‘now’: “All attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of times, viz., of simultaneity, unrecognizedly was anchored in the unconscious. Clearly to recognize this axiom and its arbitrary character really implies already the solution of the problem.”

Einstein’s original 1905 paper begins with a lengthy discussion, practically free of equations, of the physical operations involved in synchronizing clocks at distant points. He then shows that these same operations, implemented by a moving system of observers, lead to differing determinations of which events occur “at the same time”.
As relativity undermines ‘now’, quantum theory undermines ‘here’. Heisenberg had Einstein’s analysis specifically in mind when, in the opening of his seminal paper on the new quantum mechanics in 1925, he advocated the formulation of physical laws using observable quantities only. But while classical theory has a naive conception of a particle’s position, described by a single coordinate (a triple of numbers, for three- dimensional space), quantum theory requires this to be replaced by a much more abstract quantity. One aspect of the situation is that if you don’t measure the position, you must not assume that it has a definite value. Many successful calculations of physical processes using quantum mechanics are based on performing a precise form of averaging over many different positions where a particle “might be found”.  These calculations would be ruined if you assumed that the particle was always at some definite place. You can choose to measure its position, but performing such a measurement involves disturbing the particle. It changes both the question and the answer.

Einstein himself was never reconciled to the loss of ‘here’. In his greatest achievement, the general theory of relativity, Einstein relied heavily on the primitive notions of events in space-time and (proper) distance between nearby events. These notions rely on unambiguous association of times and spaces — ‘nows’ and ‘heres’ — to individual objects of reality (though not, of course, on the existence of a universal ‘now’). Understandably impressed by the success of his theory, Einstein was loath to sacrifice its premises. He resisted modern quantum theory, and held aloof from its sweeping success in elucidating problem after great problem.

Ironically, the sacrifice he feared has not (yet) proved necessary. On the contrary, in the modern theory of Matter, we retain ‘nows’ and ‘heres’ for the fundamental objects of reality. These primitives are no less important in the formulation of the subatomic laws of quantum theory than in general relativity. The new feature is that the fundamental objects of reality are one step removed from the directly observed: they are quantum fields, rather than physical events.

It is possible to avoid ordinary language and its snares. Within specific domains of mathematics, this is accomplished by constructing exact definitions and axioms. Purity of language is also forced on us when we interact with modern digital computers, since they do not tolerate ambiguity.

But the purity of artificial language comes at a great cost in scope, suppleness and flexibility. Perhaps computers will become truly intelligent when they learn to be tolerant of ordinary, sloppy language — and then to use it themselves! In any case, for us humans the practical and wise course will be to continue to use ordinary language, even for abstract scientific investigations, but to be very suspicious of it. Along these lines, Heisenberg’s considered formulation, put forward in the Physical Principles of Quantum Theory in 1930, was: “It is found advisable to introduce a great wealth of concepts into a physical theory, without attempting to justify them rigorously, and then to allow experiment to decide at what points a revision is necessary.”

Looking to the future, after ‘now’ and ‘here’, what basic intuition will next acquire reformation? As the nature of mind comes into scientific focus, might it be ‘I’? Perhaps the following remarks of Hermann Weyl, stimulated by deep reflection on the aspects of modern physics discussed here and stated in his Philosophy of Mathematics and Natural Science (1949), point in that direction: “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along the life line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.”

Reference
1. Einstein, A., “Autobiographical notes”, in Albert Einstein, Philosopher-Scientist, ed. Schilpp, P. (Library of Living Philosophers, 1949).

from: Fantastic Realities, Frank Wilczek (Nobel Prize in Physics, 2004)

also: When words fail, Frank Wilczek, Nature 410, 149 (2001). https://doi.org/10.1038/35065756

PhD Thesis

Those who know the letters see double [twice as much as those who don't]

(Greek inscription at the Old College, University of Edinburgh)

Four Obvious Rules for Choosing a Thesis Topic:

1. The topic should reflect your previous studies and experience. It should be related to your completed courses; your other research; and your political, cultural, or religious experience.

2. The necessary sources should be materially accessible. You should be near enough to the sources for convenient access, and you should have the permission you need to access them.

3. The necessary sources should be manageable. In other words, you should have the ability, experience, and background knowledge needed to understand the sources.

4. You should have some experience with the methodological framework that you will use in the thesis. For example, if your thesis topic requires you to analyze a Bach violin sonata, you should be versed in music theory and analysis.

Umberto Eco

Knowledge

The tree of knowledge (Monk of Mount Athos) / © National Geographic

The endless cycle of idea and action,
Endless invention, endless experiment,
Brings knowledge of motion, but not of stillness;
Knowledge of speech, but not of silence;
Knowledge of words, and ignorance of the Word.
All our knowledge brings us nearer to our ignorance,
All our ignorance brings us nearer to death,
But nearness to death no nearer to God.
Where is the Life we have lost in living?
Where is the wisdom we have lost in knowledge?
Where is the knowledge we have lost in information?

Thomas Stearns Eliot [Choruses from the Rock, 1934]

Creative

Pacific Ocean, California / © I.A. Daglis

If you want to be creative, then you will have to get used to spending most of your time not being creative, to being becalmed on the ocean of scientific knowledge.

Steven Weinberg [Nobel Prize in Physics 1979, in Four golden lessons, Nature, 27 November 2003]

Knowledge

No one knows everything, and you don’t have to.

Steven Weinberg [Nobel Prize in Physics, 1979]
in Four golden lessons, Nature, 27 November 2003

Erkenntnis - Knowledge

Fortune teller in Bangkok

"Wo der Baum der Erkenntnis steht, ist immer das Paradies": so reden die ältesten und die jüngsten Schlangen.

"Where the tree of knowledge stands is always paradise": that 's what the oldest and the most recent serpents declare.

Friedrich Nietzsche [Jenseits von Gut und Böse, Aphorismus 152, 1886]

Science limits

Limits / © I.A. Daglis

Science itself, as it advances, keeps imposing limits on its own power. Einstein’s theory of special relativity prohibits the transmission of matter or even information at speeds faster than that of light; quantum mechanics dictates that our knowledge of the microrealm will always be uncertain; chaos theory confirms that even without quantum indeterminacy many phenomena would be impossible to predict; Kurt Gödel’s incompleteness theorem denies us the possibility of constructing a complete, consistent mathematical description of reality. And evolutionary biology keeps reminding us that we are animals, designed by natural selection not for discovering deep truths of nature, but for breeding.

John Horgan [The End of Science, 1996]