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Posts Tagged ‘complexity

“Man is not born to solve the problem of the universe, but to find out what he has to do; and to restrain himself within the limits of his comprehension”*…

 

Half a century ago, the pioneers of chaos theory discovered that the “butterfly effect” makes long-term prediction impossible. Even the smallest perturbation to a complex system (like the weather, the economy or just about anything else) can touch off a concatenation of events that leads to a dramatically divergent future. Unable to pin down the state of these systems precisely enough to predict how they’ll play out, we live under a veil of uncertainty.

But now the robots are here to help…

In new computer experiments, artificial-intelligence algorithms can tell the future of chaotic systems.  For example, researchers have used machine learning to predict the chaotic evolution of a model flame front like the one pictured above.  Learn how– and what it may mean– at “Machine Learning’s ‘Amazing’ Ability to Predict Chaos.”

* Johann Wolfgang von Goethe

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As we contemplate complexity, we might recall that it was on this date in 1961 that Robert Noyce was issued patent number 2981877 for his “semiconductor device-and-lead structure,” the first patent for what would come to be known as the integrated circuit.  In fact another engineer, Jack Kilby, had separately and essentially simultaneously developed the same technology (Kilby’s design was rooted in germanium; Noyce’s in silicon) and had filed a few months earlier than Noyce… a fact that was recognized in 2000 when Kilby was Awarded the Nobel Prize– in which Noyce, who had died in 1990, did not share.

Noyce (left) and Kilby (right)

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“To imagine a language is to imagine a form of life”*…

 

Jeremy England is concerned about words—about what they mean, about the universes they contain. He avoids ones like “consciousness” and “information”; too loaded, he says. Too treacherous. When he’s searching for the right thing to say, his voice breaks a little, scattering across an octave or two before resuming a fluid sonority.

His caution is understandable. The 34-year-old assistant professor of physics at the Massachusetts Institute of Technology is the architect of a new theory called “dissipative adaptation,” which has helped to explain how complex, life-like function can self-organize and emerge from simpler things, including inanimate matter. This proposition has earned England a somewhat unwelcome nickname: the next Charles Darwin. But England’s story is just as much about language as it is about biology…

A new theory on the emergence of life’s complexity: “How Do You Say ‘Life’ in Physics?

* Ludwig Wittgenstein, Philosophical Investigations

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As we resist the urge to simplify, we might send carefully-constructed birthday greetings to Sir Karl Raimund Popper; he was born on this date in 1902.  One of the greatest philosophers of science of the 20th century, Popper is best known for his rejection of the classical inductivist views on the scientific method, in favor of empirical falsification: A theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can and should be scrutinized by decisive experiments. (Or more simply put, whereas classical inductive approaches considered hypotheses false until proven true, Popper reversed the logic: conclusions drawn from an empirical finding are true until proven false.)

Popper was also a powerful critic of historicism in political thought, and (in books like The Open Society and Its Enemies and The Poverty of Historicism) an enemy of authoritarianism and totalitarianism.

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Written by LW

July 28, 2017 at 1:01 am

“I’m not afraid of death; I just don’t want to be there when it happens”*…

 

The life expectancy for the average woman in the United States is 81 years and 2 months. For men, it’s 76 years and 5 months. These are the most recent estimates from the Centers for Disease Control and Prevention. Just subtract your current age from those numbers for a rough estimate of how many years you have left.

It feels accurate. It feels precise.

But people die at various ages. Life is imprecise. Otherwise, you could just plan your days all the way up to your last.

Also, life expectancy is typically quoted “from birth.” It’s the number of years a baby is expected to live the moment he or she escapes from the womb into the wondrous realities of the outside world. This is a good measure for progress in countries and is a fine wideout view, but it’s just so-so for you and me, as individuals.

The range of your life expectancy is much more interesting…

See for yourself:  toggle to your gender and age on Flowing Data‘s interactive graphic (based on data from the Social Security Administration), and see the “Years You Have Left to Live, Probably.”

* Woody Allen

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As we memento mori, we might spare a thought for Giambattista Vico; he died on this date in 1744. A political philosopher, rhetorician, historian, and jurist, Vico was one of the greatest Enlightenment thinkers. Best known for the Scienza Nuova (1725, often published in English as New Science), he famously criticized the expansion and development of modern rationalism and was an apologist for classical antiquity.

He was an important precursor of systemic and complexity thinking (as opposed to Cartesian analysis and other kinds of reductionism); and he can be credited with the first exposition of the fundamental aspects of social science, though his views did not necessarily influence the first social scientists.  Vico is often claimed to have fathered modern philosophy of history (although the term is not found in his text; Vico speaks of a “history of philosophy narrated philosophically”). While he was not strictly speaking a historicist, interest in him has been driven by historicists (like Isaiah Berlin).

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Written by LW

January 23, 2016 at 1:01 am

From the Department of Stating the Obvious…

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From AAAS’ Science, “It’s Official: Physics is Hard“:

Students and researchers alike have long understood that physics is challenging. But only now have scientists managed to prove it. It turns out that one of the most common goals in physics—finding an equation that describes how a system changes over time—is defined as “hard” by computer theory. That’s bad news for physics students who hope that a machine can solve all their homework problems, but at least their future jobs in the field are safe from automation.

Physicists are often interested in mathematically describing how a system behaves: for instance, a formula tracks the motions of the planets and their moons in their complicated dance around the sun. Researchers work out these equations by measuring the objects at various points in time and then developing a formula that links all of those points together, such as filling in a video from a set of snapshots.

With each new variable, however, it becomes tougher to find the right equation. Computers can speed things up by sifting through potential solutions at breakneck speed, but even the world’s top supercomputers meet their match with a certain class of problems, known as “hard” problems. These problems take exponentially more time to solve with every additional variable that is thrown into the mix—an extra planet’s motion, for instance…

[Full article here]

Problems like these, known in complexity theory as NP-hard, may be discouraging of the prospect of quick solutions; but at least they seem to offer physicists some measure of job security.  Still, if a bankable short-cut could be found, it would have profound implications for math and it applications.  So the Clay Mathematics Institute has chosen the challenge as one of its Millennium Problems:  the scientist who comes up with a universal “problem tenderizer” wins $1 million.

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As we remember that pie are square, we might spare a memorial thought for the polymathic John Arbuthnot; he died on this date in 1735.  The mathematician, essayist, and physician published his translation of Huygens’ Of the Laws of Chance (1692), to which Arbuthnot added further games of chance– the first work on probability published in English.  He wrote a series of satirical pamphlets introducing “john Bull” (the now-iconic “Englishman”), and co-founded Scriblerus Club, where he inspired co-founders Jonathan Swift (Gulliver’s Travels book III) and Alexander Pope (Peri Bathous, Or the Art of Sinking in PoetryMemoirs of Martin Scriblerus, and The Dunciad).  And from 1705, he was physician to Queen Anne until her death in 1714.

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Written by LW

February 27, 2012 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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