Descartes’s changing mind

Descartes is always concerned about knowledge. However, the Galileo affair in 1633, the reactions to his Discourse on method, and later his need to reply to objections to his Meditations provoked crises in Descartes’s intellectual development the import of which has not been sufficiently recognized. These events are the major reasons why Descartes’s philosophical position concerning how we know and what we may know is radically different at the end of his life from what it was when he began. We call this later position Descartes’s epistemic stance and contrast it with his earlier methodological, metaphysical realism. Yet Descartes’s epistemic views cannot be separated from other aspects of his work, for example, his views concerning God, causality, metaphysics, and the nature of science. A further meta-implication is that serious errors await any scholar who cites early Cartesian texts in support of late Cartesian positions, or who uses later texts in conjunction with early ones to support a reading of Descartes’s philosophy.     

Mutation of the matrix metalloproteinase 2 gene (MMP2) causes a multicentric osteolysis and arthritis syndrome.

The inherited osteolyses or 'vanishing bone' syndromes are a group of rare disorders of unknown etiology characterized by destruction and resorption of affected bones. The multicentric osteolyses are notable for interphalangeal joint erosions that mimic severe juvenile rheumatoid arthritis (OMIMs 166300, 259600, 259610 and 277950). We recently described an autosomal recessive form of multicentric osteolysis with carpal and tarsal resorption, crippling arthritic changes, marked osteoporosis, palmar and plantar subcutaneous nodules and distinctive facies in a number of consanguineous Saudi Arabian families. We localized the disease gene to 16q12-21 by using members of these families for a genome-wide search for homozygous-by-descent microsatellite markers. Haplotype analysis narrowed the critical region to a 1.2-cM region that spans the gene encoding MMP-2 (gelatinase A, collagenase type IV; (ref. 3). We detected no MMP2 enzymatic activity in the serum or fibroblasts of affected family members. We identified two family-specific homoallelic MMP2 mutations: R101H and Y244X. The nonsense mutation effects a deletion of the substrate-binding and catalytic sites and the fibronectin type II-like and hemopexin/TIMP2 binding domains. Based on molecular modeling, the missense mutation disrupts hydrogen bond formation within the highly conserved prodomain adjacent to the catalytic zinc ion.     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Why the Afshar experiment does not refute complementarity

A modified version of Young's experiment by Shahriar Afshar demonstrates that, prior to what appears to be a “which-way” measurement, an interference pattern exists. Afshar has claimed that this result constitutes a violation of the Principle of Complementarity. This paper discusses the implications of this experiment and considers how Cramer's Transactional Interpretation easily accommodates the result. It is also shown that the Afshar experiment is analogous in key respects to a spin one-half particle prepared as “spin up along x”, subjected to a nondestructive confirmation of that preparation, and post-selected in a specific state of spin along z. The terminology “which-way” or “which-slit” is critiqued; it is argued that this usage by both Afshar and his critics is misleading and has contributed to confusion surrounding the interpretation of the experiment. Nevertheless, it is concluded that Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and post-selection spin experiment, in which the particle's preparation state is confirmed by a nondestructive measurement prior to post-selection. In addition, some new inferences about the interpretation of delayed choice experiments are drawn from the analysis.     

Using genetically-defined rodent strains for the identification of hippocampal traits relevant for two-way avoidance behavior: a non-invasive approach

Summary Genetically-defined rodent strains permit the identification of hippocampal traits which are of functional relevance for the performance of two-way avoidance behavior. This is exemplified here by analyzing the relationship between infrapyramidal mossy fibers (a tiny projection terminating upon the basal dendrites of hippocampal pyramidal neurons) and two-way avoidance learning in about 800 animals. The necessary steps include 1) identification of structural traits sensitive to selective breeding for extremes in two-way avoidance, 2) testing the robustness of the associations found by studying individual and genetical correlations between hippocampal traits and behavior, 3) establishing causal relationships by Mendelian crossing of strains with extreme structural traits and studying the behavioral consequences of such structural randomization, 4) confirming causal relationships by manipulating the structural variable in inbred (isogenic) strains, thereby eliminating the possibility of genetic linkage, and 5) ruling out the possibility of spurious associations by studying the correlations between the hippocampal trait and other behaviors known to depend on hippocampal functioning.In comparison with the classical lesion approach for identifying relationships between brain and behavior, the present procedure appears to be superior in two aspects: it is non-invasive, and it focuses automatically on those brain traits which are used by natural selection to shape behaviorally-defined animal populations, i.e., it reveals the natural regulators of behavior.     

Clustering the rows and columns of a contingency table

A number of ways of investigating heterogeneity in a two-way contingency table are reviewed. In particular, we consider chi-square decompositions of the Pearson chi-square statistic with respect to the nodes of a hierarchical clustering of the rows and/or the columns of the table. A cut-off point which indicates significant clustering may be defined on the binary trees associated with the respective row and column cluster analyses. This approach provides a simple graphical procedure which is useful in interpreting a significant chi-square statistic of a contingency table.The author gratefully acknowledges the constructive comments of the referees and the editor.     

The contents of the pygidial gland of the primitive antNothomyrmecia macrops (Hymenoptera:Formicidae)

Summary The principal constituent of the pygidial gland ofNothomyrmecia macrops is 3,7-dimethyloct-6-en-2-one, a substance not previously identified in insects. Also identified were 2,6-dimethylhept-5-enal, 2-nonanone, indole, -dodecalactone, and the hydrocarbons pentadecane, heptadecane, heptadecene and heptadecadiene, all in low nanogram quantities.     

Lack of effect of dihydroergotamine on endothelial and smooth muscle cell proliferation and endothelial cell prostanoid production

Summary The most important effect of dihydroergotamine is venoconstriction, but certain metabolic effects and changes in vessel prostanoid activity have also been suggested. In this study endothelial cell production of 6-keto PGF₁ and TxB₂ was quantitated in vitro. No evidence of altered prostanoid production was noted after incubation with dihydroergotamine (exposure ranging from 5×10^–3 to 5×10^–7 g/l). Similarly, no effect of dihydroergotamine on the growth rates of endothelial cells or smooth muscle cells in vitro was documented.     

Inhibition by tetanus and botulinum A toxin of the release of [3H]noradrenaline and [3H]GABA from rat brain homogenate

Summary Rat brain homogenate was preloaded with [³H]noradrenaline or [³H]GABA and stimulated with high K⁺. Tetanus toxin and botulinum A neurotoxin partially prevent the evoked [³H]noradrenaline release in the same range of toxin concentrations starting below 10^–10M. In contrast, release of -amino butyric acid (GABA) is much more sensitive to tetanus than to botulinum A toxin.     

Pharmacodynamic profile of CQP 201-403, a novel 8α-amino-ergoline

Summary The profile of action in animals of CQP 201-403, a novel 8-amino-ergoline, is in most aspects that of a very potent dopaminomimetic, both as a prolactin secretion inhibitor, and at the levels of the CNS and the cardiovascular system. Qualitatively CQP 201-403 differs slightly from bromocriptine and apomorphine in its effects on the CNS (no influence on serotonin metabolism in the rat cortex; induction of masculine mounting behavior in rats) and the cardiovascular system of the dog (reflex tachycardia in response to a blood-pressure fall). In man the new compound proved to be highly active in lowering prolactin serum levels and to be more potent than bromocriptine (Parlodel^®).In memory of Dr Annemarie Closse, who died 14 June 1987.