Why We Walk the Way We Do

By using inverse dynamics and forceplate recordings, this study established the principle of oscillating systems and the influence of gravity and body parameters on the programming of the gait parameters, step frequency and length. Calculation of the ratio of the amplitude of the center of mass (CM) and the center of foot pressure (CP) oscillations yielded an equation and established a biomechanical constant, the natural body frequency (NBF). NBF appears to be an absolute invariant parameter, specific to human standing posture and gait in terrestrial gravity, which influences the relative positions of CM and CP and whose value separates the frequency bands of standing posture from those for gait. This equation was tested by using the experimental paradigm of stepping in place and then used in calculating the magnitude of CM oscillations during gait. The biomechanical analysis of the experimental observations allows one to establish the relationships between body parameters and gravity and the central programming of locomotor parameters.     

Postural Requirements and Progression Velocity in Young Walkers

This article describes developmental changes in gait velocity and relates these changes to gait parameters that index postural stability (step width and lateral acceleration) and two components of velocity (cadence and step length).

Five children were observed longitudinally over a 2-year period after onset of independent walking. Their range of speed increased threefold in the first 6 months of independent walking and then remained constant. In contrast, step width decreased approximately twofold. Whereas in adults, cadence and step length contribute approximately equally to speed, when infants first begin to walk independently, increase in velocity is due mostly to increased step length. After 5 months of independent walking, the pattern reverses, and increase in velocity is due primarly to increased cadence. The pattern remains constant over the next 18 months. From a developmental point of view, the data lead us to interpret early walking (the first 5 months) as a process of integration of postural constraints into the dynamic necessities of gait movement. A second phase, beginning after 4 to 5 months of independent walking, is considered to be a tuning phase characterized by a more precise adjustment of the gait parameters.     

Hermann Weyl on Minkowskian Space–Time and Riemannian Geometry

Hermann Weyl as a founding father of field theory in relativistic physics and quantum theory always stressed the internal logic of mathematical and physical theories. In line with his stance in the foundations of mathematics, Weyl advocated a constructivist approach in physics and geometry. An attempt is made here to present a unified picture of Weyl’s conception of space–time theories from Riemann to Minkowski. The emphasis is on the mathematical foundations of physics and the foundational significance of a constructivist philosophical point of view. I conclude with some remarks on Weyl’s broader philosophical views.     

Why we walk the way we do

By using inverse dynamics and forceplate recordings, this study established the principle of oscillating systems and the influence of gravity and body parameters on the programming of the gait parameters, step frequency and length. Calculation of the ratio of the amplitude of the center of mass (CM) and the center of foot pressure (CP) oscillations yielded an equation and established a biomechanical constant, the natural body frequency (NBF). NBF appears to be an absolute invariant parameter, specific to human standing posture and gait in terrestrial gravity, which influences the relative positions of CM and CP and whose value separates the frequency bands of standing posture from those for gait. This equation was tested by using the experimental paradigm of stepping in place and then used in calculating the magnitude of CM oscillations during gait. The biomechanical analysis of the experimental observations allows one to establish the relationships between body parameters and gravity and the central programming of locomotor parameters.     

Hilbert and the internal logic of mathematics

Hilbert's programme is shown to have been inspired in part by what we can call Kronecker's programme in the foundations of an arithmetic theory of algebraic quantities.While finitism stays within the bounds of intuitive finite arithmetic, metamathematics goes beyond in the hope of recovering classical logic. The leap into the transfinite proved to be hazardous, not only from the perspective of Gödel's results, but also from a Kroneckerian point of view.Hilbert's rare admission of a Kroneckerian influence does not constitute the basis of such a reconstruction; it is rather Kronecker's mathematical practice which is seen as a forerunner of Hilbert's endeavour in the foundations of mathematics.I am indebted to an anonymous referee for many helpful critical remarks.     

Control of gait initiation

The initiation of gait from a standing posture by 6 subjects, who took controlled-length steps, was analyzed. Using an inverted pendulum model, we found that the duration of gait initiation was independent of gait velocity. This finding suggests that subjects' biomechanical constants are the determining factors for initiating movement. Both the instantaneous velocity of the center of gravity at the end of the first step (resulting in the propulsive forces measured on the ground) and the steady-state velocity (resulting in the step length and frequency) varied with step length, whereas step frequency did not. But step frequency and progression velocity were linked, for step frequency always increased in parallel with increased progression velocity. We interpret the correlation between velocity and frequency variations to be a peripheral expression of the posturodynamic control of the step parameters by the progression forces.     

ETUDE INTERCULTURELLE DE LA GENERALISATION DES OPERATIONS: SIMILITUDE ET COHERENCE DES ACTIVITES DE CLASSIFICATION ET DE SERIATION CHEZ DES SUJETS CANADIENS-FRANÇAIS,RWANDAIS SCOLARISES ET RWANDAIS NON SCOLARISES*

Sixty-two French-Canadian children, seven to ten years old; 64 schooled Rwandese children, ten to thirteen years old; and 32 unschooled Rwandese subjects aged 15 and 17 were tested on four piagetian logico-mathematical tasks: hierarchical classification (CA), multiple classification (CM), seriation of weight (RA) and double seriation (RM). Due to the effect of order, separate analyses were performed for tasks done during the same test session. When the results of tasks CA and RM, on the one hand, and of RA and CM, on the other hand, are combined, it is observed, firstly, that the items alternate in order of difficulty and, secondly, that the number of coherent patterns of responses exceeds the null hypothesis in French-Canadian and schooled Rwandese populations, supporting the hypothesis of a complementary and partially synchronous modality of structuration of logical abilities. From another point of view, when the items from all four tasks are combined in a single scale of difficulty, the very close similarity observed between the ranks of the items in the three populations strengthens the hypothesis of a universally determined cognitive development based mainly on the equilibration process.     

The mind of global human society. A new approach to investigating the future

In this essay, I present a new approach, called “ideometry,” which may lead to a new way of integrating knowledge and investigating the future of scientific conceptions. Conceptions are examined in themselves, independently of the reality they are supposedly describing. This is done formally by means of a new concept, “alterity.” A consequence of this formal consideration is a possible “super‐mind” of global human society, a very large and complex, growing system, analogous to a child's brain.     

Control of Gait Initiation

The initiation of gait from a standing posture by 6 subjects, who took controlled-length steps, was analyzed. Using an inverted-pendulum model, we found that the duration of gait initiation was independent of gait velocity. This finding suggests that subjects' biomechanical constants are the determining factors for initiating movement. Both the instantaneous velocity of the center of gravity at the end of the first step (resulting in the propulsive forces measured on the ground) and the steady-state velocity (resulting in the step length and frequency) varied with step length, whereas step frequency did not. But step frequency and progression velocity were linked, for step frequency always increased in parallel with increased progression velocity. We interpret the correlation between velocity and frequency variations to be a peripheral expression of the posturodynamic control of the step parameters by the progression forces.