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Posts Tagged ‘dimensionality

“Above all else show the data”*…

 

With the hope that your celebrations will be warm and peaceful, and with thanks for your kind attention over the last twelve months, (Roughly) Daily is going on it’s annual Holiday hiatus…  So here, to tide us over, The Economist Graphics Unit’s wonderful “2017 Daily chart advent calendar” (the first installment of which, above)– a collection of 25 of the years best infographics, each with a short accompanying essay.

See you in the New Year!

* Edward Tufte

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As we revel in new ways of seeing, we might send terrifyingly (and at the same time, amusingly) insightful birthday greetings to Edwin Abbott; he was born on this date in 1838.  A schoolmaster and theologian, Abbott is best remembered as the author of the remarkable novella Flatland: A Romance of Many Dimensions (1884). Writing pseudonymously as “A Square,” Abbott used the fictional two-dimensional world of Flatland to offer pointedly-satirical observations on the social hierarchy of Victorian culture. But the work has survived– and inspired legions of mathematicians and science fiction writers– by virtue of its fresh and accessible examination of dimensionality.  Indeed, Flatland was largely ignored on its original publication; but it was re-discovered after Einstein’s General Theory of Relativity– which posits a fourth dimension– was introduced; in a 1920 letter to Nature, Abbott is called a prophet for his intuition of the importance of time to explain certain phenomena.

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Written by LW

December 20, 2017 at 1:01 am

Adventures in Cosmology: Starting out Simply…

Why was entropy so low at the Big Bang? (source: Internet Encyclopedia of Philosophy)

Back in 2010, SUNY-Buffalo physics professor Dejan Stojkovic and colleagues made a simple– a radically simple– suggestion:  that the early universe — which exploded from a single point and was very, very small at first — was one-dimensional (like a straight line) before expanding to include two dimensions (like a plane) and then three (like the world in which we live today).

The core idea is that the dimensionality of space depends on the size of the space observed, with smaller spaces associated with fewer dimensions. That means that a fourth dimension will open up — if it hasn’t already — as the universe continues to expand.  (Interesting corollary: space has fewer dimensions at very high energies of the kind associated with the early, post-big bang universe.)

Stojkovic’s notion is challenging; but at the same time, it would help address a number of fundamental problems with the standard model of particle physics, from the incompatibility between quantum mechanics and general relativity to the mystery of the accelerating expansion of the universe.

But is it “true”?  There’s no way to know as yet.  But Stojkovic and his colleagues have devised a test using the Laser Interferometer Space Antenna (LISA), a planned international gravitational observatory, that could shed some definitive light on the question in just a few years.

Read the whole story in Science Daily, and read Stojkovic’s proposal for experimental proof in Physical Review Letters.

As we glance around for evidence of that fourth dimension, we might bid an indeterminate farewell to Ilya Prigogine, the Nobel Laureate whose work on dissipative structures, complex systems, and irreversibility led to the identification of self-organizing systems, and is seen by many as a bridge between the natural and social sciences.  He died at the Hospital Erasme in Brussels on this date in 2003.

Prigogine’s 1997 book, The End of Certainty, summarized his departure from the determinist thinking of Newton, Einstein, and Schrödinger in arguing for “the arrow of time”– and “complexity,” the ineluctable reality of irreversibility and instability.  “Unstable systems” like weather and biological life, he suggested, cannot be explained with standard deterministic models.  Rather, given their to sensitivity to initial conditions, unstable systems can only be explained statistically, probabilistically.

source: University of Texas

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