1,528 research outputs found
Letters to Joel
A professor and his students answer his brother’s question: Is mathematics art
The Deconstruction of Mathematics: A criticism of Reuben Hersh\u27s What Is Mathematics, Really? and the Humanist Philosophy of Mathematics
Mathematics, as an academic discipline, has stood for many years as the last bastion against a growing tide of intellectual relativism that has become all but ubiquitous. More recently, however, efforts have been made to humanize mathematics by advocating a social-constructivist approach to the philosophy of mathematics, both in practice and education. This paper is intended to serve as a critical response to one advocate of this approach, Reuben Hersh (What Is Mathematics, Really?, 1997), and in the process a defense of Platonism
Mathematics As Worship
This paper treats worship in a broad, inclusive sense as the primary and necessary response of human beings to their creator. It provides a brief overview of the relationship between mathematics and theology from the Pythagoreans to the present. It argues that all knowledge is contingent upon faith and thus that contemplation of mathematical insights can lead to worship of God
The Hidden Injuries Of Overloading \u27ADT
The most commonly stated definition of abstract data type (ADT) is that it is a domain of values and the operations over that domain. So, for example, a language\u27s built-in types, like int are seen to be ADTs. It is our opinion that a pure interpretation of this definition yields a semantics in which using an ADT is the same as using built-in types: the operations are side effect free and there is no concern over alias, shallow copy or synchronization problems. Unfortunately, the term abstract data type has over time been associated with at least three distinct meanings, and those incompatible definitions have often been conflated, causing confusion to students and textbook authors alike. We believe that this has resulted in a loss of appreciation for the value-based semantics of ADTs
Experimental ancilla-assisted qubit transmission against correlated noise using quantum parity checking
We report the experimental demonstration of a transmission scheme of photonic
qubits over unstabilized optical fibers, which has the plug-and-play feature as
well as the ability to transmit any state of a qubit, regardless of whether it
is known, unknown, or entangled to other systems. A high fidelity to the
noiseless quantum channel was achieved by adding an ancilla photon after the
signal photon within the correlation time of the fiber noise and by performing
quantum parity checking. Simplicity, maintenance-free feature and robustness
against path-length mismatches among the nodes make our scheme suitable for
multi-user quantum communication networks.Comment: 8 pages, 4 figures; published in New J. Phys. and selected in IOP
Selec
Unusual behaviour of the ferroelectric polarization in PbTiO/SrTiO superlattices
Artificial PbTiO/SrTiO superlattices were constructed using
off-axis RF magnetron sputtering. X-ray diffraction and piezoelectric atomic
force microscopy were used to study the evolution of the ferroelectric
polarization as the ratio of PbTiO to SrTiO was changed. For
PbTiO layer thicknesses larger than the 3-unit cells SrTiO
thickness used in the structure, the polarization is found to be reduced as the
PbTiO thickness is decreased. This observation confirms the primary role
of the depolarization field in the polarization reduction in thin films. For
the samples with ratios of PbTiO to SrTiO of less than one a
surprising recovery of ferroelectricity that cannot be explained by
electrostatic considerations was observed
High rate, long-distance quantum key distribution over 250km of ultra low loss fibres
We present a fully automated quantum key distribution prototype running at
625 MHz clock rate. Taking advantage of ultra low loss fibres and low-noise
superconducting detectors, we can distribute 6,000 secret bits per second over
100 km and 15 bits per second over 250km
- …