PLato said,"Look to the perfection of the heavens for truth," while Aristotle said "look around you at what is, if you would know the truth" To Remember: Eskesthai
The last major changes to the periodic table was done in the middle of the 20th Century. Glenn Seaborg is given the credit for it. Starting with his discovery of plutonium in 1940, he discovered all the transuranic elements from 94 to 102. He reconfigured the periodic table by placing the actinide series below the lanthanide series. In 1951, Seaborg was awarded the Noble prize in chemistry for his work. Element 106 has been named seaborgium (Sg) in his honor.A BRIEF HISTORY OF THE DEVELOPMENT OF PERIODIC TABLE
"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Harold Scott Macdonald (H. S. M.) Coxeter
In my perspective the Platonic solids were a first attempt at trying to describe reality?
Holding these thoughts I had a bit of time to think as to how one might go about this other then the ways on which we have particularize the particles of energy collisions that are decay products of the energy involved? I understand what he is saying so the following was sure to follow.
So many thoughts go through my mind not just of the orbitals or Bohr's model, but of how we might have looked at new elements created to have them classed in Mendeleev's the table of elements. Describing these elemental signatures to have them assigned a space" in between" of those we have already mapped.
Proceedings of Societies [Report on the Law of Octaves]
The shapes of the first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz. The colors show the wave function phase. These are graphs of ψ(x,y,z) functions which depend on the coordinates of one electron. To see the elongated shape of ψ(x,y,z)2 functions that show probability density more directly, see the graphs of d-orbitals below.
The shapes of atomic orbitals can be understood qualitatively by considering the analogous case of standing waves on a circular drum.[19] To see the analogy, the mean vibrational displacement of each bit of drum membrane from the equilibrium point over many cycles (a measure of average drum membrane velocity and momentum at that point) must be considered relative to that point's distance from the center of the drum head. If this displacement is taken as being analogous to the probability of finding an electron at a given distance from the nucleus, then it will be seen that the many modes of the vibrating disk form patterns that trace the various shapes of atomic orbitals. The basic reason for this correspondence lies in the fact that the distribution of kinetic energy and momentum in a matter-wave is predictive of where the particle associated with the wave will be. That is, the probability of finding an electron at a given place is also a function of the electron's average momentum at that point, since high electron momentum at a given position tends to "localize" the electron in that position, via the properties of electron wave-packets (see the Heisenberg uncertainty principle for details of the mechanism).
This relationship means that certain key features can be observed in both drum membrane modes and atomic orbitals. For example, in all of the modes analogous to s orbitals (the top row in the illustration), it can be seen that the very center of the drum membrane vibrates most strongly, corresponding to the antinode in all s orbitals in an atom. This antinode means the electron is most likely to be at the physical position of the nucleus (which it passes straight through without scattering or striking it), since it is moving (on average) most rapidly at that point, giving it maximal momentum.
A mental "planetary orbit" picture closest to the behavior of electrons in s orbitals, all of which have no angular momentum, might perhaps be that of the path of an atomic-sized black hole, or some other imaginary particle which is able to fall with increasing velocity from space directly through the Earth, without stopping or being affected by any force but gravity, and in this way falls through the core and out the other side in a straight line, and off again into space, while slowing from the backwards gravitational tug. If such a particle were gravitationally bound to the Earth it would not escape, but would pursue a series of passes in which it always slowed at some maximal distance into space, but had its maximal velocity at the Earth's center (this "orbit" would have an orbital eccentricity of 1.0). If such a particle also had a wave nature, it would have the highest probability of being located where its velocity and momentum were highest, which would be at the Earth's core. In addition, rather than be confined to an infinitely narrow "orbit" which is a straight line, it would pass through the Earth from all directions, and not have a preferred one. Thus, a "long exposure" photograph of its motion over a very long period of time, would show a sphere.
In order to be stopped, such a particle would need to interact with the Earth in some way other than gravity. In a similar way, all s electrons have a finite probability of being found inside the nucleus, and this allows s electrons to occasionally participate in strictly nuclear-electron interaction processes, such as electron capture and internal conversion.
Below, a number of drum membrane vibration modes are shown. The analogous wave functions of the hydrogen atom are indicated. A correspondence can be considered where the wave functions of a vibrating drum head are for a two-coordinate system ψ(r,θ) and the wave functions for a vibrating sphere are three-coordinate ψ(r,θ,φ)
s-type modes
Mode u01 (1s orbital)
Mode u02 (2s orbital)
Mode u03 (3s orbital)
p-type modes
Mode u11 (2p orbital)
Mode u12 (3p orbital)
Mode u13 (4p orbital)
d-type modes
Mode u21 (3d orbital)
Mode u22 (4d orbital)
Mode u23 (5d orbital)
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So yes understanding that if you had Einstein crossing the room it becomes important to wonder about what gathering capabilities allow such elements to form other then students. You are looking for something specific?
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String theory isn't just another quantum field theory, another particular finite list of elementary particles with some interactions. It's an intellectually and literally multi-dimensional reservoir of wisdom that has taught us many things of completely new kinds that we couldn't foresee.The Reference Frame: LHC: is a new particle?: LHC: is χb(3P) a new particle?
practically nobody took very seriously the CDF claim.......Tommaso: I will claim based on the above that according to Prof. D'Agostini, Prof. Matt Strassler is "practically nobody", since he is not convinced.
An acoustical difference of opinion with regard too, Nobody?
Hmmmmm.......One is a shop keeper and one is a customer?
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Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. To evaluate the probability of a hypothesis, the Bayesian probabilist specifies some prior probability, which is then updated in the light of new, relevant data.[1]
The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation. Bayesian probability interprets the concept of probability as " a probability p is an abstract concept, a quantity that we assign theoretically, for the purpose of representing a state of knowledge, or that we calculate from previously assigned probabilities,"[2] in contrast to interpreting it as a frequency or a "propensity" of some phenomenon.
The term "Bayesian" refers to the 18th century mathematician and theologian Thomas Bayes (1702–1761), who provided the first mathematical treatment of a non-trivial problem of Bayesian inference.[3] Nevertheless, it was the French mathematician Pierre-Simon Laplace (1749–1827) who pioneered and popularised what is now called Bayesian probability.[4]
Broadly speaking, there are two views on Bayesian probability that interpret the probability concept in different ways. According to the objectivist view, the rules of Bayesian statistics can be justified by requirements of rationality and consistency and interpreted as an extension of logic.[2][5] According to the subjectivist view, probability measures a "personal belief".[6] Many modern machine learning methods are based on objectivist Bayesian principles.[7] In the Bayesian view, a probability is assigned to a hypothesis, whereas under the frequentist view, a hypothesis is typically tested without being assigned a probability.
The sequential use of the Bayes' formula: when more data become available after calculating a posterior distribution, the posterior becomes the next prior.
In frequentist statistics, a hypothesis is a proposition (which must be either true or false), so that the (frequentist) probability of a frequentist hypothesis is either one or zero. In Bayesian statistics, a probability can be assigned to a hypothesis.
Objective and subjective Bayesian probabilities
Broadly speaking, there are two views on Bayesian probability that interpret the 'probability' concept in different ways. For objectivists, probability objectively measures the plausibility of propositions, i.e. the probability of a proposition corresponds to a reasonable belief everyone (even a "robot") sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by requirements of rationality and consistency.[2][5] Requirements of rationality and consistency are also important for subjectivists, for which the probability corresponds to a 'personal belief'.[6] For subjectivists however, rationality and consistency constrain the probabilities a subject may have, but allow for substantial variation within those constraints. The objective and subjective variants of Bayesian probability differ mainly in their interpretation and construction of the prior probability.
In the 20th century, the ideas of Laplace were further developed in two different directions, giving rise to objective and subjective currents in Bayesian practice. In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed.[11] No subjective decisions need to be involved. In contrast, "subjectivist" statisticians deny the possibility of fully objective analysis for the general case.
In the 1980s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to the discovery of Markov chain Monte Carlo methods, which removed many of the computational problems, and an increasing interest in nonstandard, complex applications.[12] Despite the growth of Bayesian research, most undergraduate teaching is still based on frequentist statistics.[13] Nonetheless, Bayesian methods are widely accepted and used, such as in the fields of machine learning[7] and talent analytics.
Richard T. Cox showed that[5] Bayesian updating follows from several axioms, including two functional equations and a controversial hypothesis of differentiability. It is known that Cox's 1961 development (mainly copied by Jaynes) is non-rigorous, and in fact a counterexample has been found by Halpern.[14] The assumption of differentiability or even continuity is questionable since the Boolean algebra of statements may only be finite.[15] Other axiomatizations have been suggested by various authors to make the theory more rigorous.[15]
Dutch book approach
The Dutch book argument was proposed by de Finetti, and is based on betting. A Dutch book is made when a clever gambler places a set of bets that guarantee a profit, no matter what the outcome is of the bets. If a bookmaker follows the rules of the Bayesian calculus in the construction of his odds, a Dutch book cannot be made.
However, Ian Hacking noted that traditional Dutch book arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books. For example, Hacking writes[16] "And neither the Dutch book argument, nor any other in the personalist arsenal of proofs of the probability axioms, entails the dynamic assumption. Not one entails Bayesianism. So the personalist requires the dynamic assumption to be Bayesian. It is true that in consistency a personalist could abandon the Bayesian model of learning from experience. Salt could lose its savour."
In fact, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on "probability kinematics" following the publication of Richard C. Jeffrey's rule). The additional hypotheses sufficient to (uniquely) specify Bayesian updating are substantial, complicated, and unsatisfactory.[17]
Decision theory approach
A decision-theoretic justification of the use of Bayesian inference (and hence of Bayesian probabilities) was given by Abraham Wald, who proved that every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.[18] Conversely, every Bayesian procedure is admissible.[19]
Personal probabilities and objective methods for constructing priors
Following the work on expected utilitytheory of Ramsey and von Neumann, decision-theorists have accounted for rational behavior using a probability distribution for the agent. Johann Pfanzagl completed the Theory of Games and Economic Behavior by providing an axiomatization of subjective probability and utility, a task left uncompleted by von Neumann and Oskar Morgenstern: their original theory supposed that all the agents had the same probability distribution, as a convenience.[20] Pfanzagl's axiomatization was endorsed by Oskar Morgenstern: "Von Neumann and I have anticipated" the question whether probabilities "might, perhaps more typically, be subjective and have stated specifically that in the latter case axioms could be found from which could derive the desired numerical utility together with a number for the probabilities (cf. p. 19 of The Theory of Games and Economic Behavior). We did not carry this out; it was demonstrated by Pfanzagl ... with all the necessary rigor".[21]
Ramsey and Savage noted that the individual agent's probability distribution could be objectively studied in experiments. The role of judgment and disagreement in science has been recognized since Aristotle and even more clearly with Francis Bacon. The objectivity of science lies not in the psychology of individual scientists, but in the process of science and especially in statistical methods, as noted by C. S. Peirce.[citation needed] Recall that the objective methods for falsifying propositions about personal probabilities have been used for a half century, as noted previously. Procedures for testing hypotheses about probabilities (using finite samples) are due to Ramsey (1931) and de Finetti (1931, 1937, 1964, 1970). Both Bruno de Finetti and Frank P. Ramsey acknowledge[citation needed] their debts to pragmatic philosophy, particularly (for Ramsey) to Charles S. Peirce.
The "Ramsey test" for evaluating probability distributions is implementable in theory, and has kept experimental psychologists occupied for a half century.[22] This work demonstrates that Bayesian-probability propositions can be falsified, and so meet an empirical criterion of Charles S. Peirce, whose work inspired Ramsey. (This falsifiability-criterion was popularized by Karl Popper.[23][24])
Modern work on the experimental evaluation of personal probabilities uses the randomization, blinding, and Boolean-decision procedures of the Peirce-Jastrow experiment.[25] Since individuals act according to different probability judgements, these agents' probabilities are "personal" (but amenable to objective study).
Personal probabilities are problematic for science and for some applications where decision-makers lack the knowledge or time to specify an informed probability-distribution (on which they are prepared to act). To meet the needs of science and of human limitations, Bayesian statisticians have developed "objective" methods for specifying prior probabilities.
Indeed, some Bayesians have argued the prior state of knowledge defines the (unique) prior probability-distribution for "regular" statistical problems; cf. well-posed problems. Finding the right method for constructing such "objective" priors (for appropriate classes of regular problems) has been the quest of statistical theorists from Laplace to John Maynard Keynes, Harold Jeffreys, and Edwin Thompson Jaynes: These theorists and their successors have suggested several methods for constructing "objective" priors:
Each of these methods contributes useful priors for "regular" one-parameter problems, and each prior can handle some challenging statistical models (with "irregularity" or several parameters). Each of these methods has been useful in Bayesian practice. Indeed, methods for constructing "objective" (alternatively, "default" or "ignorance") priors have been developed by avowed subjective (or "personal") Bayesians like James Berger (Duke University) and José-Miguel Bernardo (Universitat de València), simply because such priors are needed for Bayesian practice, particularly in science.[26] The quest for "the universal method for constructing priors" continues to attract statistical theorists.[26]
Thus, the Bayesian statistican needs either to use informed priors (using relevant expertise or previous data) or to choose among the competing methods for constructing "objective" priors.
See also
Bertrand's paradox: a paradox in classical probability, solved by E.T. Jaynes in the context of Bayesian probability
De Finetti's game – a procedure for evaluating someone's subjective probability
^ abc Jaynes, E.T. "Bayesian Methods: General Background." In Maximum-Entropy and Bayesian Methods in Applied Statistics, by J. H. Justice (ed.). Cambridge: Cambridge Univ. Press, 1986
^ Stigler, Stephen M. (1986) The history of statistics. Harvard University press. pg 131.
^ Stigler, Stephen M. (1986) The history of statistics., Harvard University press. pg 97-98, pg 131.
^ abc Cox, Richard T. Algebra of Probable Inference, The Johns Hopkins University Press, 2001
^ ab de Finetti, B. (1974) Theory of probability (2 vols.), J. Wiley & Sons, Inc., New York
^ ab Bishop, C.M. Pattern Recognition and Machine Learning. Springer, 2007
^ ab Bernardo, J. M. (2005). Reference Analysis. Handbook of Statistics 25 (D. K. Dey and C. R. Rao eds). Amsterdam: Elsevier, 17-90
References
Berger, James O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer Series in Statistics (Second ed.). Springer-Verlag. ISBN0-387-96098-8.
de Finetti, Bruno. "Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science," (translation of 1931 article) in Erkenntnis, volume 31, September 1989.
de Finetti, Bruno (1937) "La Prévision: ses lois logiques, ses sources subjectives," Annales de l'Institut Henri Poincaré,
de Finetti, Bruno. "Foresight: its Logical Laws, Its Subjective Sources," (translation of the 1937 article in French) in H. E. Kyburg and H. E. Smokler (eds), Studies in Subjective Probability, New York: Wiley, 1964.
de Finetti, Bruno (1974–5). Theory of Probability. A Critical Introductory Treatment, (translation by A.Machi and AFM Smith of 1970 book) 2 volumes. Wiley ISBN 0471201413, ISBN 0471201421
Hacking, Ian (December 1967). "Slightly More Realistic Personal Probability". Philosophy of Science34 (4): 311–325. doi:10.1086/288169. JSTOR186120. Partly reprinted in: Gärdenfors, Peter and Sahlin, Nils-Eric. (1988) Decision, Probability, and Utility: Selected Readings. 1988. Cambridge University Press. ISBN 0521336589
Hajek, A. and Hartmann, S. (2010): "Bayesian Epistemology", in: Dancy, J., Sosa, E., Steup, M. (Eds.) (2001) A Companion to Epistemology, Wiley. ISBN 1405139005Preprint
Hald, Anders (1998). A History of Mathematical Statistics from 1750 to 1930. New York: Wiley. ISBN0471179124.
Hartmann, S. and Sprenger, J. (2011) "Bayesian Epistemology", in: Bernecker, S. and Pritchard, D. (Eds.) (2011) Routledge Companion to Epistemology. Routledge. ISBN 10415962196 (Preprint)
McGrayne, Sharon Bertsch. (2011). The Theory That Would Not Die: How Bayes' Rule Cracked The Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of Controversy. New Haven: Yale University Press. 13-ISBN 9780300169690/10-ISBN 0300169698; OCLC 670481486
Morgenstern, Oskar (1978). "Some Reflections on Utility". In Andrew Schotter. Selected Economic Writings of Oskar Morgenstern. New York University Press. pp. 65–70. ISBN9780814777718.
Pfanzagl, J (1967). "Subjective Probability Derived from the Morgenstern-von Neumann Utility Theory". In Martin Shubik. Essays in Mathematical Economics In Honor of Oskar Morgenstern. Princeton University Press. pp. 237–251.
Pfanzagl, J. in cooperation with V. Baumann and H. Huber (1968). "Events, Utility and Subjective Probability". Theory of Measurement. Wiley. pp. 195–220.
Ramsey, Frank Plumpton (1931) "Truth and Probability" (PDF), Chapter VII in The Foundations of Mathematics and other Logical Essays, Reprinted 2001, Routledge. ISBN 0415225469,
Stigler, Stephen M. (1990). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press/Harvard University Press. ISBN0-674-40341-X.
Stigler, Stephen M. (1999) Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press. ISBN 0-674-83601-4
December 15, 2011: The bipolar star-forming region, called Sharpless 2-106, or S106 for short, looks like a soaring, celestial snow angel. The outstretched "wings" of the nebula record the contrasting imprint of heat and motion against the backdrop of a colder medium. Twin lobes of super-hot gas, glowing blue in this image, stretch outward from the central star. This hot gas creates the "wings" of our angel. A ring of dust and gas orbiting the star acts like a belt, cinching the expanding nebula into an "hourglass" shape. See: Hubble Serves Up a Holiday Snow Angel
“On average, new Kreutz-group comets are discovered every few days by SOHO, but from the ground they are much rarer to see or discover,” says Karl Battams, Naval Research Laboratory, who curates the Sun-grazing comets webpage. See Also: The beginning of the end for comet Lovejoy
One instrument watching for the comet was the Solar Dynamics Observatory (SDO), which adjusted its cameras in order to watch the trajectory. Not only does this help with comet research, but it also helps orient instruments on SDO -- since the scientists know where the comet is based on other spacecraft, they can finely determine the position of SDO's mirrors. This first clip from SDO from the evening of Dec 15, 2011 shows Comet Lovejoy moving in toward the sun.
Comet Lovejoy survived its encounter with the sun. The second clip shows the comet exiting from behind the right side of the sun, after an hour of travel through its closest approach to the sun. By tracking how the comet interacts with the sun's atmosphere, the corona, and how material from the tail moves along the sun's magnetic field lines, solar scientists hope to learn more about the corona. This movie was filmed by the Solar Dynamics Observatory in 171 Angstrom wavelength, which is typically shown in yellow.
Although Aristotle in general had a more empirical and experimental attitude than Plato, modern science did not come into its own until Plato's Pythagorean confidence in the mathematical nature of the world returned with Kepler, Galileo, and Newton. For instance, Aristotle, relying on a theory of opposites that is now only of historical interest, rejected Plato's attempt to match the Platonic Solids with the elements -- while Plato's expectations are realized in mineralogy and crystallography, where the Platonic Solids occur naturally.Plato and Aristotle, Up and Down-Kelley L. Ross, Ph.D.
I enjoyed the Livescribe demonstration by Clifford of Asymptotia along with the explanation for Quantum Gravity. The two pillars for me were very emblematic with regards to "pillars of science." This as well as the arch is very fitting to me of what becomes self evident. If under such an examination of the two areas Clifford is talking about, Quantum Mechanics and General Relativity then are the attempts at unification.
Fermilab scientist Don Lincoln describes the concept of how the search for the Higgs boson is accomplished. The latest data is revealed! Several large experimental groups are ht on the trail of this elusive subatomic particle which is thought to explain the origins of particle mass.
