The bear, says Hierocles, is aware that its head is easily injured, and instinctively uses its paws as a protection. The three following lines in the papyrus are badly damaged– καν εί π.ε … δεηθεί Του | βαλανεíον κρημν | πáλιν ύ;β εθεíησιν ε | αυΤήν. This is followed by a description of what the bear does when it is pursued and comes to a precipice. It inflates itself and trusts to the inflation to break its fall. It is hardly (...) possible to restore the damaged lines. Von Arnim thinks that the sense required is: ‘wenn die Bärin, vom Jäger verfolgt, eines Bades bedarf oder auf ihrer Flucht an einen Abgrund kommt,πáλιν ύπ èψίησιν εαψτήν’ But a sensible bear would hardly think of taking a bath when pursued by the hunter. It might take to the water; but the Greek for this would be somewhat different. As I read the passage, there is no reference to the bear as pursued by the hunter till line 34, where I would read πоιεî δè τò τοιóνδε , since the phrase εί δ υν διοκμéνμ in line 38 is resumptive, and implies that the pursuit must have been alluded to before. But before line 35 H. is only describing what the bear does to protect its head in the ordinary routine of its life when it is not harassed by the hunter. It wants a bath, and finds that it cannot reach the water without clambering down an overhanging bank It will not climb down head foremost, but guards its head by sliding backwards down the bank. As the bear would want its bath because it was hot, it is perhaps not too hazardous to conjecture that some phrase such as xs03F0xs2135ν ει π ε<ζομéν πνíγηι δεμθεíν του β. should find its place in line 31. (shrink)

The issue of energy and its potential localizability in general relativity has challenged physicists for more than a century. Many non-invariant measures were proposed over the years but an invariant measure was never found. We discovered the invariant localized energy measure by expanding the domain of investigation from space to spacetime. We note from relativity that the finiteness of the velocity of propagation of interactions necessarily induces indefiniteness in measurements. This is because the elements of actual physical systems being measured (...) as well as their detectors are characterized by entire four-velocity fields, which necessarily leads to information from a measured system being processed by the detector in a spread of time. General relativity adds additional indefiniteness because of the variation in proper time between elements. The uncertainty is encapsulated in a generalized uncertainty principle, in parallel with that of Heisenberg, which incorporates the localized contribution of gravity to energy. This naturally leads to a generalized uncertainty principle for momentum as well. These generalized forms and the gravitational contribution to localized energy would be expected to be of particular importance in the regimes of ultra-strong gravitational fields. We contrast our invariant spacetime energy measure with the standard 3-space energy measure which is familiar from special relativity, appreciating why general relativity demands a measure in spacetime as opposed to 3-space. We illustrate the misconceptions by certain authors of our approach. (shrink)

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes (...) attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism. (shrink)

Originally published in 1920 as part of a series of handbooks for teachers, this book of advice to history teachers is still full of practical information on the use of historical sources and possible classroom exercises designed to engage children with the study of the past. This book will be useful to anyone with an interest in the history of education, historical education in particular.

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