Content uploaded by E. Danezis
Author content
All content in this area was uploaded by E. Danezis on Aug 19, 2014
Content may be subject to copyright.
From Phytagoreans to Kepler: the dispute between the geocentric and the heliocentric systems
Abstract
Some ancient Greek philosophers and thinkers questioned the geocentric system and proposed instead a heliocentric system. The main proponents of this view - which was seen as heretical at the time - are believed to have been the Pythagoreans Philolaos, Heraclides, Hicetas, and Ecphantos, but mainly Aristarchos of Samos, who placed the Sun in the position of the "central fire" of the Pythagoreans. The geocentric system, reworked by Claudius Ptolemaeus (Ptolemy), was the dominant one for centuries, and it was only during the sixteenth century that the Polish monk-astronomer, Copernicus, revisited the ancient Greek heliocentric views and became the new champion of the theory that we all accept today.
... Aristarchos the Samian ("Αρίσταρχος ο Σάμιος"), followed the teachings of Pythagoreans who were the first -back in the 6 th century B.C.-to question the geocentric theory and formed the hypothesis of the heliocentric system. He also proposed the simultaneous rotation of the Earth around its axis on a daily basis and its movement in a circular orbit around the Sun on an annual basis [137]. ...
New smart meters, distributed generation, renewable energy sources and the concern about the environment are redefining the way to conceive and operate electrical grids. To take full advantage of the new electrical smart grids we need to monitor and protect them. The capability of self-healing is thus important in smart grids in order to ensure a proper behavior under faults and reduce power outage times. For this purpose, this thesis proposes three different methods of fault diagnosis for low voltage (LV) distribution grids and two methods of fault isolation for grid-connected photovoltaic systems (GCPVs).In electrical power distribution systems, faults are responsible for 80% of customer interruptions. While several fault location methods for distribution grids exist in the literature, the majority of them focuses on medium voltage grids and low fault resistance values that rarely surpass the 100 Ohms. Taking into account that distribution system operators usually rely on phone calls to detect and locate faults in LV grids, the need for fault detection and location techniques that cover these cases, i.e. large fault resistances and LV distribution grids, is evident.The three fault detection and location methods proposed in this thesis are:1.A conventional fault detection method based on overcurrent monitoring in combination with a method that uses sparse voltage measurements to build the voltage profile across the faulty branch for fault location.2.Gradient boosting trees(GBT), a method that has been proven to excel in many applications the last few years.3.Deep neural networks(DNN), a method that improve the traditional neural network architecture by taking advantage of an increased number of hidden layers.Simulations on a real semi-rural LV distribution grid of Portugal are performed to validate the results. A common case study is used to compare the three methods. The influencing parameters are: a) a big variety of fault resistance values (63,772 values between 1 and 1000 Ohms), b) nine different fault locations within each sector, c) two fault types (single phase to ground and three phase faults), d) a simultaneity factor of 0.5, e) a big spectrum of PV generation and load demand scenarios with 70,334 studied combinations and f) a 2% underestimation error in measurements.Overall, DNN are the most reliable solution demonstrating a 100% accuracy in fault detection and an average of 12% of error in distance estimation. Moreover, under the minimum available measurements (on at the beginning of the feeder and one at each terminal node) case their accuracy is decreased by only 4.5%.At the same time, faults in PV generators, present an increased interest as well. A big variety of faults can occur in a PV power plant. Based on their location faults can appear: a) in the PV array, b) in the power converters, c) on the dc bus and d) in the grid side. The development of fast, efficient and reliable fault detection and isolation methods for GCPVs, capable of dealing with the different types of faults, is a recognized necessity from the scientific community and a prerequisite for their integration in the smart grids.So far, to the author’s knowledge, no research has been found to monitor the GCPV as a complete system, i.e. isolating faults in every part of the plant with a single method. For this reason, two algorithms based on a signal approach are proposed as a fault isolation strategy. They use current and voltage measurements at the output of the inverter, examining faults occurring on all four of the aforementioned possible locations. The choice of the output of the inverter, i.e. the point of common coupling, as the monitoring source of the status of the GCPV system is in accordance with the location of voltage sensors used in the previous case of fault location methods in the LV distribution grid. Finally, the proposed algorithms achieve an isolation of 15 out of the 19 studied faults cases in less than 100 ms.
... An instance of this theme is the heliocentric vs. geocentric view of the solar system. Before the heliocentric viewpoint was widely accepted, scholars had already worked out the movements of the planets [1]. The main contribution of the new perspective was that now the planetary trajectories were simple ellipses instead of more complicated movements involving loops 2 . ...
We examine the influence of input data representations on learning complexity. For learning, we posit that each model implicitly uses a candidate model distribution for unexplained variations in the data, its noise model. If the model distribution is not well aligned to the true distribution, then even relevant variations will be treated as noise. Crucially however, the alignment of model and true distribution can be changed, albeit implicitly, by changing data representations. "Better" representations can better align the model to the true distribution, making it easier to approximate the input-output relationship in the data without discarding useful data variations. To quantify this alignment effect of data representations on the difficulty of a learning task, we make use of an existing task complexity score and show its connection to the representation-dependent information coding length of the input. Empirically we extract the necessary statistics from a linear regression approximation and show that these are sufficient to predict relative learning performance outcomes of different data representations and neural network types obtained when utilizing an extensive neural network architecture search. We conclude that to ensure better learning outcomes, representations may need to be tailored to both task and model to align with the implicit distribution of model and task.
... Their counterpart polymaths of the Islamic scientific heritage played also such a most significant historical role for the transmission and development of knowledge. The "Little Renaissance" of the 12th century, and the Age of Renaissance in the 14th century in Europe, both seem to originate from this fountain of Knowledge and great Personalities [11], [12]. ...
... The only significant deviation from the Ptolemaic paradigm is the assumption and the theoretical embracement of the Heliocentric paradigm, as already stated within the work of Aristarchus of Samos, which is surely a great achievement of first order (Theodossiou et al., 2002). On the other hand, all the information and the tools for managing both the theoretical aspects of this astronomical theory, as well as for extrapolating the planetary positions on their orbits, that is the handling of the empirical data, is of the same complexity as the one which characterizes the Ptolemaic paradigm, to which we shall refer in the forthcoming paragraph. ...
... Kepler is convinced that the Copernican heliocentric model of the Universe corresponds in an absolute and definite manner to the physical reality and enriches the Copernican Paradigm with the statement of his Science Publications AJSS eponymous three Laws of planetary motion, an ingenious labor which served as one of the key elements for Newton to derive his own Theory of Gravity (Theodossiou et al., 2002). Kepler, in his attempt, combines the Christian Neoplatonic elements of a Geometrized Universe with his novel approach of a Dynamical Cosmos driven by specific Laws of Nature. ...
... Their counterpart polymaths of the Islamic scientific heritage played also such a most significant historical role for the transmission and development of knowledge. The "Little Renaissance" of the 12th century, and the Age of Renaissance in the 14th century in Europe, both seem to originate from this fountain of Knowledge and great Personalities [11], [12]. ...
The place of Johannes Kepler in Astronomy is specified from both directions in historical time. The first refers explicitly to the world – picture of the polymaths and astronomers before his era, and the second to the novel world – picture of the scholars and philosophers that succeeded him.
