Akadeemia
Eurozine
Akadeemia
2011-11-11
Abstracts for Akadeemia 11/2011
Taivo Liiva
The mystical forces of inertia
One of the most intriguing questions in classical mechanics is the meaning and impact of the inertia force. Is this force real or fictitious? In the opinion of believers in the fictitiousness of the inertia force, the inertia force ma balances, according to Newton's second law F = ma, the sum F of all real forces affecting a mass point. Actually, there is no balance as the mass point moves with acceleration a. Thus, the balance is only imaginary or formal, and the inertia force should also be fictitious. Up until now, most textbooks have not treated the qualitative aspect of the inertia force, and even lecturers or professors of physics have not reached a common consensus on how to interpret this force.
If the inertia force has an impact on the bonds restricting the movement (e.g. the right bank of a flowing river in the northern hemisphere of the Earth), then what does that force impact if such bonds are lacking (e.g. in the case of the free fall of a body to the Earth)? Is the force of inertia still real?
Regardless of the rotation of the Earth, the body will fall in the same way, and the deviation in relation to the Earth is a simple kinematic phenomenon. In understanding it, Albert Einstein's discovery that gravity and inertia are the same phenomenon is helpful. This phenomenon does not depend on the qualities of the body itself but on the peculiarities of the space surrounding it. Thus, we reach Einstein's famous principle of equivalence which states: in a sufficiently small part of space, no physical experiments enable us to differentiate between the movement of a body on the impact of forces of gravity from its movement in an acceleratingly moving frame of reference.
Thus, if gravity and inertia are the same phenomenon, the fictitiousness of the inertia force would also mean the fictitiousness of the force of gravity, and resulting from that, the fictitiousness of the whole Universe.
The article also provides an overview of the history of Baer's law, actually Baer-Babinet's law, which states that, because of the rotation of the Earth, a body moving on the surface of the Earth in the northern hemisphere deviates from the direction of its movement to the right, in the southern hemisphere, however, to the left. Differently from several other authoritative encyclopaedias, the Estonian Encyclopaedia calls Baer's law Baer-Babinot's law, which is fully justified.
Timothy Gowers
The work of John Milnor
In addition to many other research awards, Milnor has received the Abel Prize. One of the most important concepts in mathematics the manifold. To get an idea of what a manifold is, one should think of the surface of a sphere, or of a torus. If one looks at a very small area of such a surface, its geometry is just like the ordinary two-dimensional geometry of the plane, which goes back to Euclid. However, the global behaviour of manifolds is not Euclidean.
Another aspect of the manifold is that it is possible to talk about manifolds intrinsically. That is, one can discuss the geometry of a manifold by mentioning just the points in the manifold itself and making no reference to any external space inside which the manifold lives. Secondly, there can be manifolds of any dimension. The third point is essential background to one of John Milnor's most remarkable results: The main characteristic feature of a manifold, that its geometry is locally just like Euclidean geometry, can have several different notions, two of which are essential here. The first notion comes from topology: we say that two shapes are homeomorphic if each one is a continuous deformation of the other. The second notion comes from calculus: two shapes are diffeomorphic if they are not just continuous deformations of each other but differentiable deformations of each other. A differentiable deformation is "smoother" than a continuous one is required to be -- folds, corners and sharp bends are disallowed. In 1956, Milnor found an extraordinary mathematical object: a shape that is homeomorphic to a seven-dimensional sphere but not diffeomorphic to it.
The fact that manifolds could be homeomorphic but not diffeomorphic means that the differentiable manifold is an important object in its own right and not just a way of looking at a topological manifold. For this reason, Milnor's construction gave birth to a whole new field of mathematics known as differential topology which includes several other highlights of modern mathematics.
Gowers rounds off by describing some other findings by John Milnor: the Hauptvermutung (German for "main conjecture") or the question whether any two triangulations have a common refinement; in the area of parallelizable spheres a new proof to the hairy ball theorem; a solution to the question how curved a knot should be; algebraic K-theory and holomorphic dynamics.
Enn Kasak
On religiosity in science
It seems to be usual that scientists are not alert to their religious beliefs or do not consider them essential, although in the opinion of some researchers (e.g. R. A. Clouser) it is impossible to discuss any scientific theory adequately without considering its religious aspects.
Kasak concentrates on critical reactions that the expression religiosity in science elicits among scientists and science philosophers. Rational arguments have been taken from the critiques against using this expression and are discussed in a logical order where each following point of the critique becomes a subject of the discussion after answering the critique in the previous point. The discussion of religion and religiosity in the context of science poses at least six kinds of problems: definition, field of meaning, existence, relevance, purpose and methodology.
The main points are:
(1) There are beliefs in science that, in their essence, resemble religious beliefs, and to refer to them it is expedient to use the term religiosity in science.
(2) The term religiosity in science is rather unpopular among scientists but arguments against the use of such a term can be systematized and, in turn, criticized.
(3) Research into religiosity of science is necessary. Scientists should become aware of the existence of such a phenomenon; this might be one of the facets in the development of self-awareness in science.
(4) Religiosity in science can also have a positive meaning. An informed choice of whether to acknowledge one's belief or not is of great significance in the research activities of the scientist as a person and in his/her ethical attitudes to science.
(5) Religiosity of science can be studied scientifically. Using the methodologies elaborated for this, it is also possible to study scientifically some other interesting aspects of religiosity, e.g. religiosity in politics, economy, etc.
Perhaps it would be time to discard the religious attitude according to which there can be no religiosity in science whatsoever, and to treat this phenomenon as another object of philosophical analysis and scientific research.
Ilmar Raag
Can smoking be condemned?: Misunderstanding, talking at cross-purposes and loss in translation
Raag's article is the continuation of a study from the University of Georgia (Athens) that revealed that in the case of some anti-smoking advertisements, even an increase in smoking could be noted in the target group. One explanation for this is that in language each meaning exists virtually always together with its opposite meaning. In real communication, however, the opposite meaning of the meaning is activated if the target group perceives the sender of the message as a representative of a hostile or unreliable community. As present-day societies are very heterogeneous, every message moving in the public space can have different interpretations.
Raag presents the hypothesis that each message automatically creates a negative interpretation among at least 10 per cent of the population, while the proportion of population agreeing with a message is seldom higher than 30 per cent. To prove his argument, Raag views the numbers of supporting votes for political parties in society, maximum viewer ratings of television programmes and attendance records of films in relation to the total population. The existence of an opposite interpretation also poses an essential ethical question: "Is it possible to speak about things society wants to get rid of if merely speaking about them makes people react opposite to what is desired?" The pragmatic approach says that one should consider whether the social capital of people agreeing with the message is greater than that of those who are opposed to the message. If the social capital of people agreeing with a message is greater, then a positive effect is possible, but in all cases the emergence of an opposing interpretation should be taken into account.
Mikael Laidre
In defence of the Middle Ages. II. A: Late Antiquity
The concept of Late Antiquity as a bridge of continuity between classical antiquity and the Middle Ages has come under systematic attack by some scholars. This is similar to the vilification of the Middle Ages which has entered common parlance. Ever since the emergence of the humanists, Late Antiquity has been subjected to arbitrary interpretation. This periodical phenomenon has always been a mirror of a certain present, artificial attribution of contemporary problems to the past, instead of an objective historia or scientific inquiry. For this reason, Late Antiquity and the Middle Ages need defending. What is lacking is an objective treatment of the period which would establish its worth in itself also in contrast to modernity instead of trying to defend it by making it look as modern as possible.
What is crucial is that the core areas of the Roman Empire in the West remained highly civilized despite changes and transformations, and even crises. Additionally, new areas and peoples who had so far eluded Roman control and had therefore naturally been nowhere near levels of classical Graeco-Roman development, came under the cultural, religious, linguistic, economic, legal and political influence of a Christian and Graeco-Roman joint civilization which later came to be identified as Europe. Only those parts of the Near East and North Africa that were lost to Islam experienced decline and fall.
The positive vocabulary of continuity and transformation that has come under attack should also be liberated from seemingly neutral attempts at hijacking these terms as milder, politically more correct and not-so-ubiquitous alternatives for decline and fall. Laidre argues for the understanding that continuity and transformation really mean both stability and development, i.e. the preservation, spread and progress of civilization.
Madis Kõiv
Class 10b
In his memoirs Kõiv describes his studies in post-war Estonia, at Tartu Secondary School No. 1 (now known under its earlier name of Hugo Treffner Gymnasium). He observes both his schoolmates and teachers, sometimes also describing their later destinies. Participation in the school's physics circle was not insignificant either -- this led to his academic career and post of leading research fellow in theoretical physics.
The memoirs also hint at the strengthening grip of the Soviet occupation -- the teachers' self-censorship. Kõiv does not describe repressions in detail, instead he concentrates on the students' interests and their mutual relations.