Many have the intuition that for a conditional to be true, there must exist some kind of connection between its antecedent and its consequent. We investigated experimentally the prospects for spelling out the connection in terms of inference. Participants were shown or given by description a series of fourteen numbered color patches ranging from blue to green. They were then asked to evaluate c...

There is a strong tendency in science to opt for simpler and more unified hypotheses. A view that has often been voiced is that such qualities, though aesthetically pleasing or beautiful, are at best pragmatic considerations in matters of choosing between rival hypotheses. This essay offers a novel conception and an associated measure of unification, both of which are manifestly more than just ...

It is proved that the phase shift of a polarized neutron interacting with a spatially uniform time-dependent magnetic field, demonstrates the same physical principles as the magnetic Aharonov-Bohm effect. The crucial role of inert objects is explained, thereby proving the quantum mechanical nature of the effect. It is also proved that the nonsimply connectedness of the fieldfree region is not a...

where I denotes the class of dendrites, II is the regular curves, III is the hereditarily locally connected continua, IV is the rational curves, and V» is the class of continua of dimension not exceeding n. Now it should be remarked that, for each of these classes save the first, if a continuum possesses the defining property in the small then it is a member of the class. That is, a local regul...

We survey some of the topological properties of the attractors of iterated function systems such as connectedness, arcwise connectedness and locally arcwise connectedness. We give necessary and sufficient conditions for the attractors of finite iterated function system (IFS) to be a connected sets and in the case when infinite iterated function systems (IIFS) are considered we give only some su...

In the beginning of article we show some consequences of the regularity axiom. In the second part we introduce the successor of a set and the notions of transitivity and connectedness wrt membership relation. Then we define ordinal numbers as transitive and connected sets, and we prove some theorems of them and of their sets. Lastly we introduce the concept of a transfinite sequence and we show...

The spaces of conformally equivalent Riemann surfaces, Mg where g ≥ 1, are not manifolds. However the spaces of the weaker Teichmüller equivalence, Tg are known to be manifolds. The Teichmüller space Tg is the universal covering of Mg and Mg is the quotient space by the action of the modular group. This gives Mg an orbifold structure with a branch locus Bg . The branch loci Bg can be identified...

Let K,L,M be orthogonal projections of a point P onto the sides of a triangle ABC. Then the locus of P such that K,L,M are collinear, is the circumcircle of ABC. This theorem has several generalizations [4], [5], [10],[6], [7], [9]. A generalization of the Simson–Wallace theorem which is by [2] ascribed to J. D. Gergonne is as follows: Let K,L,M be orthogonal projections of a point P onto the s...