Autor: Vertin, Michael -- Mehrere Autoren: Lonergan Workshop, Volume 8

Buch: Lonergan's "Three Basic Questions" and a Philosophy of Philosophies

Titel: Byrne, Patrick H., Insight and the Retrieval of Nature

Stichwort: Lonergan: Natur; Schemes of Recurrence; Beispiel: Schwungrad - Carnot Kreislauf

Kurzinhalt: The notion of the scheme of recurrence arose when it was noted that the diverging series of positive conditions for an event might coil around in a circle. In that case, the series of events, A, B, C, ... would be so related that the fulfillment of ...

Textausschnitt: 2.4 Schemes of Recurrence

37b Now the statistical science of secondary determinations goes a long way towards answering the questions, "What are the other things, and how often are they equal?" But secondary determinations can also be supplied in ways which are not merely non-systematic. The first of these is the "scheme of recurrence." (Fs)

The notion of the scheme of recurrence arose when it was noted that the diverging series of positive conditions for an event might coil around in a circle. In that case, the series of events, A, B, C, ... would be so related that the fulfillment of the conditions for each would be the occurrence of the others (1958: 118). (Fs)

38a A couple of illustrations of schemes of recurrences-one an idealization of human artifact, the other recurring in nature-will connect with the previous discussion of explanatory correlations and primary relativity. (Fs)

38b The first illustration is a flywheel driven by a steam engine operating in what is known as a "Carnot cycle." The Carnot cycle has four recurrent stages, which involve changes in quantity of heat, volume, pressure, and temperature of the gas in a piston/cylinder arrangement. Schematically:

(1) The gas is compressed from its original volume (V1) to a smaller volume (V2) without loss of heat. This results in a corresponding lowering of the temperature (from T1 to T2). This is in accord with the correlation, pV = nRT. (Fs)
(2) Some heat of the piston is released, but the temperature is maintained at the constant level (T2) by allowing the volume to further contract to (V3). This is in accord both with pV = nRT, with the law of energy conservation and with the law of specific heats of gases. (Fs)
(3) The volume is now forced to expand (to V4), causing a rise in temperature (again in accord with pV = nRT). When the temperature reaches (T1), the forced expansion is stopped. (Fs)
(4) The cylinder is now heated; the temperature is maintained constant at (T1) by allowing the cylinder to further expand until it reaches the original volume, (V1); again in accord with pV = nRT, energy conservation and with the laws of specific heats. (Fs)
The cylinder and gas are now in the same state as at the beginning of stage 1, and the cycle can recur. (Fs)

38c Two distinguishable sets of determinants are required for an explanation of the sequence of events in this cycle. The first set is the classical correlations-the gas law and the laws of specific heats. The second is the propinquitous delivery of just the right values of T and V to one stage by its predecessor. This is really quite a marvelous thing, when one stops and thinks about it! If stage 1 delivered values different from T2 or V2 to stage 2, the cycle simply would follow a different, non-recurrent set of stages thereafter. (Fs)
38d The reader will also notice that this cycle is not exactly self-sufficient. It requires some "external" source to do the compressing and the forced-expanding. This is supplied by the fly-wheel connected to the piston by a drive shaft. Here yet another set of correlations is introduced, concerning the laws of torque and conservation of angular momentum. In effect, the heating and cooling of the gas drive the flywheel in stages 2 and 4, and the angular momentum of the flywheel drives the piston in stages 1 and 3. (Fs)

39a Yet this illustration does not completely eliminate the statistical. It, too, will operate only "other things being equal." The most obvious "other things" concern the delicate timing of heating and cooling. If too much heat enters or leaves in stage 2 or 4, or if any heat enters or leaves in stages 1 and 3, the cycle will fail to recur. In the world of concrete universe, these indeterminacies of the heating are responsible for the fact that this particular scheme of recurrence is so improbable that it has never been actually realized. (Fs)

39nb A second illustration is drawn from molecular biology, namely, the cycle of "oxidative phosphorylation."1 The greatest biological significance of oxidative phosphorylation consists in the fact that it results in the net production of adenosine triphosphate (ATP) molecules, which are the energy sources cells use for movement (for example, oscillation of flagella and contraction of muscle fibres), synthesis of molecules, active transport of molecules across cell membranes, nerve-impulse communication, and so on. (Fs)

One part of oxidative phosphorylation is a sequence of five chemical reactions, in which the last reaction produces one of the substrates required by the first reaction (see Figure 1). (Fs)

[...]

43a Lonergan of course provided his own series of illustrations of schemes of recurrence, beginning with the example of the "planetary system" (1958: 118). As a result, I think, the planetary system has taken on the status of a paradigmatic "scheme of recurrence," and I think this is unfortunate. The planetary system is more suggestive of a series of events which "coil around in a circle," than of a systematizing of events "related so that the fulfillment of the conditions for each would be the occurrence of the others." The circle image, together with the counterpositional pull to think primarily in terms of an imaginable "object," can make it seem that an oxidative phos-phorylation cycle does not really fulfill the definition of a scheme of recurrence, when in fact it is one of the most fruitful illustrations.1 (Fs)