Modern Platonism Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers.
September 24, by Thania Benios, University of North Carolina at Chapel Hill This artist's concept depicts a supermassive black hole at the center of a galaxy. The blue color here represents radiation pouring out from material very close to the black hole. The grayish structure surrounding the black hole, called a torus, is made up of gas and dust.
They are the ultimate unknown — the blackest and most dense objects in the universe that do not even let light escape. And as if they weren't bizarre enough to begin with, now add this to the mix: By merging two seemingly conflicting theories, Laura Mersini-Houghton, a physics professor at UNC-Chapel Hill in the College of Arts and Sciences, has proven, mathematically, that black holes can never come into being in the first place.
The work not only forces scientists to reimagine the fabric of space-time, but also rethink the origins of the universe. So the story went, an invisible membrane known as the event horizon surrounds the singularity and crossing this horizon means that you could never cross back.
It's the point where a black hole's gravitational pull is so strong that nothing can escape it. The reason black holes are so bizarre is that it pits two fundamental theories of the universe against each other.
Einstein's theory of gravity predicts the formation of black holes but a fundamental law of quantum theory states that no information from the universe can ever disappear. Efforts to combine these two theories lead to mathematical nonsense, and became known as the information loss paradox.
InStephen Hawking used quantum mechanics to show that black holes emit radiation. Since then, scientists have detected fingerprints in the cosmos that are consistent with this radiation, identifying an ever-increasing list of the universe's black holes.
But now Mersini-Houghton describes an entirely new scenario. She and Hawking both agree that as a star collapses under its own gravity, it produces Hawking radiation. However, in her new work, Mersini-Houghton shows that by giving off this radiation, the star also sheds mass.
So much so that as it shrinks it no longer has the density to become a black hole. Before a black hole can form, the dying star swells one last time and then explodes. A singularity never forms and neither does an event horizon.
The take home message of her work is clear: The paper, which was recently submitted to ArXiv, an online repository of physics papers that is not peer-reviewed, offers exact numerical solutions to this problem and was done in collaboration with Harald Peiffer, an expert on numerical relativity at the University of Toronto.
An earlier paper, by Mersini-Houghton, originally submitted to ArXiv in June, was published in the journal Physics Letters B, and offers approximate solutions to the problem. Experimental evidence may one day provide physical proof as to whether or not black holes exist in the universe.
But for now, Mersini-Houghton says the mathematics are conclusive. Many physicists and astronomers believe that our universe originated from a singularity that began expanding with the Big Bang.
However, if singularities do not exist, then physicists have to rethink their ideas of the Big Bang and whether it ever happened.Three-Minute Thesis Competition; Programs and courses Show sub-menu. Programs and courses Back ; Graduate courses; Master's Theses Robert Gooding-Townsend.
The forest transition and ecological thresholds: resilience, recovery, and predictions Department of Applied Mathematics University of Waterloo Waterloo, Ontario Canada N2L 3G1.
|Thesis Review of Related Literature Sample – Thesis Notes||Additional information You and your supervisor Before you start your Honours or Project year, you should speak to members of staff about possible thesis topics. Find out who works in the areas that you are interested in and who you find it easy to talk mathematics with.|
|Writing and numeracy||Posted on December 17, by pat thomson The conclusion is one of the most important sections of the thesis, yet it is often done quite badly. This is not good because the conclusion is a key part of the text and thesis writers really need to spend some time getting it right.|
[Business] Management, Law, or Political Science. The annual application deadline is July 9. Fulbright Foreign Student Program — Varies.
The Fulbright Foreign Student Program is a prestigious scholarship program aimed at students interested in pursuing a Master’s (or PhD) degree abroad.
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thesis Melina A Freitag Department of Mathematical Sciences University of Bath Postgraduate Away Day 3rd February 1 of The purpose of a thesis Conclusions: What have you done? Identify future research directions/open problems. 14 of Structure.
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives.
The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical. “Changes in the Land exemplifies, and realizes, the promise of ecological history with stunning effect.
Setting his sights squarely on the well-worn terrain of colonial New England, [Cronon] fashions a story that is fresh, ingenious, compelling and altogether important.