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Stability of the Solar System - Wikipedia
The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ways. For this reason (among others) the Solar System is chaotic,[1] and even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years.[2]

The Solar System is stable in human terms, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and the Earth's orbit will be relatively stable.[4]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability of the Solar System.[5]

...

The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.[3] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.[7]

Is the Solar System Stable?: https://www.ias.edu/ideas/2011/tremaine-solar-system

Is the Solar System Stable?: https://arxiv.org/abs/1209.5996
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november 2017 by nhaliday
New Theory Cracks Open the Black Box of Deep Learning | Quanta Magazine
A new idea called the “information bottleneck” is helping to explain the puzzling success of today’s artificial-intelligence algorithms — and might also explain how human brains learn.

sounds like he's just talking about autoencoders?
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september 2017 by nhaliday
Controversial New Theory Suggests Life Wasn't a Fluke of Biology—It Was Physics | WIRED
First Support for a Physics Theory of Life: https://www.quantamagazine.org/first-support-for-a-physics-theory-of-life-20170726/
Take chemistry, add energy, get life. The first tests of Jeremy England’s provocative origin-of-life hypothesis are in, and they appear to show how order can arise from nothing.
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august 2017 by nhaliday
Extended spider cognition | SpringerLink
Spiders do not seem to be cognitively limited, displaying a large diversity of learning processes, from habituation to contextual learning, including a sense of numerosity. To tease apart the central from the extended cognition, we apply the mutual manipulability criterion, testing the existence of reciprocal causal links between the putative elements of the system. We conclude that the web threads and configurations are integral parts of the cognitive systems. The extension of cognition to the web helps to explain some puzzling features of spider behaviour and seems to promote evolvability within the group, enhancing innovation through cognitive connectivity to variable habitat features. Graded changes in relative brain size could also be explained by outsourcing information processing to environmental features. More generally, niche-constructed structures emerge as prime candidates for extending animal cognition, generating the selective pressures that help to shape the evolving cognitive system.

https://www.quantamagazine.org/the-thoughts-of-a-spiderweb-20170523/
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april 2017 by nhaliday
Evolution Runs Faster on Short Timescales | Quanta Magazine
But if more splashes of paint appear on a wall, they will gradually conceal some of the original color beneath new layers. Similarly, evolution and natural selection write over the initial mutations that appear over short timescales. Over millions of years, an A in the DNA may become a T, but in the intervening time it may be a C or a G for a while. Ho believes that this mutational saturation is a major cause of what he calls the time-dependent rate phenomenon.

“Think of it like the stock market,” he said. Look at the hourly or daily fluctuations of Standard & Poor’s 500 index, and it will appear wildly unstable, swinging this way and that. Zoom out, however, and the market appears much more stable as the daily shifts start to average out. In the same way, the forces of natural selection weed out the less advantageous and more deleterious mutations over time.
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march 2017 by nhaliday
How Humans Evolved Supersize Brains | Quanta Magazine
Based on her studies, Herculano-Houzel has concluded that primates evolved a way to pack far more neurons into the cerebral cortex than other mammals did. The great apes are tiny compared to elephants and whales, yet their cortices are far denser: Orangutans and gorillas have 9 billion cortical neurons, and chimps have 6 billion. Of all the great apes, we have the largest brains, so we come out on top with our 16 billion neurons in the cortex. In fact, humans appear to have the most cortical neurons of any species on Earth. “That’s the clearest difference between human and nonhuman brains,” Herculano-Houzel says. It’s all about the architecture, not just size.
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march 2017 by nhaliday
A Unified Theory of Randomness | Quanta Magazine
Beyond the one-dimensional random walk, there are many other kinds of random shapes. There are varieties of random paths, random two-dimensional surfaces, random growth models that approximate, for example, the way a lichen spreads on a rock. All of these shapes emerge naturally in the physical world, yet until recently they’ve existed beyond the boundaries of rigorous mathematical thought. Given a large collection of random paths or random two-dimensional shapes, mathematicians would have been at a loss to say much about what these random objects shared in common.

Yet in work over the past few years, Sheffield and his frequent collaborator, Jason Miller, a professor at the University of Cambridge, have shown that these random shapes can be categorized into various classes, that these classes have distinct properties of their own, and that some kinds of random objects have surprisingly clear connections with other kinds of random objects. Their work forms the beginning of a unified theory of geometric randomness.
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february 2017 by nhaliday
In Computers We Trust? | Quanta Magazine
As math grows ever more complex, will computers reign?

Shalosh B. Ekhad is a computer. Or, rather, it is any of a rotating cast of computers used by the mathematician Doron Zeilberger, from the Dell in his New Jersey office to a supercomputer whose services he occasionally enlists in Austria. The name — Hebrew for “three B one” — refers to the AT&T 3B1, Ekhad’s earliest incarnation.

“The soul is the software,” said Zeilberger, who writes his own code using a popular math programming tool called Maple.
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january 2017 by nhaliday
The Mathematician Ken Ono’s Life Inspired By Ramanujan | Quanta Magazine
This intellectual crucible produced the desired results — Ono studied mathematics and launched a promising academic career — but at great emotional cost. As a teenager, Ono became so desperate to escape his parents’ expectations that he dropped out of high school. He later earned admission to the University of Chicago but had an apathetic attitude toward his studies, preferring to party with his fraternity brothers. He eventually discovered a genuine enthusiasm for mathematics, became a professor, and started a family, but fear of failure still weighed so heavily on Ono that he attempted suicide while attending an academic conference. Only after he joined the Institute for Advanced Study himself did Ono begin to make peace with his upbringing.
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may 2016 by nhaliday

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