o [url=www.nature.com/news/a-cellular-puzzle-the-weird-and-wonderful-architecture-of-rna-1.18014]A cellular puzzle: The weird and wonderful architecture of RNA[/url] : Nature News & Comment

Fascinating Stuff. Not sure about the crop-yield angle (though I expect much of the research funding is tied to it), though -- the last time we had a 'green revolution' it simply led to a global population boom, leaving the planet likely worse off than it would have been. And in the developed world we have way more food than we need, and waste nearly half of what we harvest and produce. So food is like money -- the problem is not that there's too little to go around, it's that its massively inequitably distributed. If saying that makes me sound like a bloody socialist and anti-free-marketeer, so be it.

o [url=http://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html]The Singular Mind of Terry Tao[/url] | NYTimes

I have a commentary on this prepared, but am interested to hear what the other math (& physics) types around think of the piece before posting my subjective take.

[QUOTE=ewmayer;406828]
o [url=http://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html]The Singular Mind of Terry Tao[/url] | NYTimes

I have a commentary on this prepared, but am interested to hear what the other math (& physics) types around think of the piece before posting my subjective take.[/QUOTE]
Of course I think he's brilliant and I appreciate his online blogging.

About Navier-Stokes, I've seen several murmurs that things are pregnant with potential progress.
Much of course involves causality and quantum-ish stuff.

[URL="https://www.quantamagazine.org/20150721-famous-fluid-equations-are-incomplete/"]Famous Fluid Equations Are Incomplete[/URL]
A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.
[QUOTE]Korteweg modeled the dynamics of fluids in which there is not only dissipation of energy (which is characterized by the Navier-Stokes equations), but also dispersion, or the smearing of energy into its component frequencies, as in a rainbow. Dissipation results from a fluid’s viscosity, or internal friction. But dispersion is caused by its capillarity — the surface tension effect that makes some liquids rise in straws. In most fluids, capillarity is negligible compared to viscosity. But it isn’t always. And mathematically, it never is. It was this capillarity, Slemrod argued in a 2012 paper, that appeared as the extra term in Karlin and Gorban’s solution to their Boltzmann-like equation. Although the finding has not yet been generalized to the full Boltzmann equation, it indicates that the particle description of a gas, when translated into a fluid description, converges not to the Navier-Stokes equations, but to the more general, far less famous Korteweg equations.[/QUOTE]
On other fronts here is a little passive robot that can do things under the influence of external magnetic fields:
[URL="http://www.dogonews.com/2015/7/28/tiny-origami-robot-runs-climbs-lifts-loads-and-even-self-destructs-once-job-is-done"]Tiny Origami Robot Runs, Climbs, Lifts Loads, And Even "Self-Destructs" Once Job Is Done[/URL]

[url]http://youtu.be/f0CluQiwLRg[/url]
[YOUTUBE]f0CluQiwLRg[/YOUTUBE]

[quote]It is common to fill page after page with an attempt, the seasons turning, only to arrive precisely where you began, empty-handed — or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematical research is to be completely stuck. It is a process that Charles Fefferman of Princeton, himself a onetime math prodigy turned Fields medalist, likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, ‘‘he crushes you.’’ So you take back moves and try something different, and he crushes you again, ‘‘in much the same way.’’ If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but — aha! — you have your first clue.[/quote]

I really, really enjoy this analogy. Quite marvelous.

When Archimedes came up with his formulae for things such as the volume of a sphere, his proofs verified that they were correct but did not show how he had arrived at the formulae in the first place. This remained a puzzle until about 100 years ago, when a reused piece of parchment was found which he had originally used for a letter to a friend. In it, he explained his reliance on physical intuition, imagining (for example) a balance with a cone hanging from one side and a sphere from the other, and what the distances would need to be for them to balance.

In the above popular article about Terry Tao, the journalist expresses surprise that ideas in engineering lead to advances in pure mathematics, but the case of Archimedes shows that this is nothing new. As Christopher Zeeman put it,
[QUOTE]Good scholars tend to compartmentalise knowledge, while researchers try to synthesise it.[/QUOTE]

Allegations of spying at the Max Planck Institute in Germany and the Technical University of Eindhoven in the Netherlands:
Press release TUE (in English): [URL]http://www.tue.nl/en/university/news-and-press/news/28-07-2015-former-employee-mentioned-in-spying-matter/[/URL]

[QUOTE=ewmayer;406828] o [URL="http://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html"]The Singular Mind of Terry Tao[/URL] | NYTimes

I have a commentary on this prepared, but am interested to hear what the other math (& physics) types around think of the piece before posting my subjective take.[/QUOTE]

He discussed a thought experiment of a machine made out of eddies in water that could make a smaller copy of itself, which could repeat ad infinitum. My though as a chemist was that it would hit a limit since you can't have an eddy smaller than one water molecule. Which should prevent the singularities in the Navier-Stokes equations from doing anything interesting (such as breaking the law of conservation of energy).

only_human's link seems to agree with this.

Chris

[QUOTE=Dubslow;406875]I really, really enjoy this analogy. Quite marvelous.[/QUOTE]

Yes, Fefferman's "chess with the devil" analogy of the process of gaining mathematical insight and proving was my favorite part of the piece.

[QUOTE=chris2be8;406904]He discussed a thought experiment of a machine made out of eddies in water that could make a smaller copy of itself, which could repeat ad infinitum. My though as a chemist was that it would hit a limit since you can't have an eddy smaller than one water molecule. Which should prevent the singularities in the Navier-Stokes equations from doing anything interesting (such as breaking the law of conservation of energy).

only_human's link seems to agree with this.

Chris[/QUOTE]

That is thinking along the same general lines as I had in mind, albeit from a microscopic rather than a macroscopic perspective. But indeed, conservation of energy is the key.

My objection is fluid-physical - here is my comment precisely as I sent to the friend who forwarded me the link over the weekend:

===================

No disrespect to Tao's mathematical abilities, but this NYT hagiography illustrates why turning basic science into a big-money contest is a horrid idea.

The specific version of N-S all the pure-math geeks are obsessing about is the [url=https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness]one posed in Millennium-prize form[/url] by the Clay Institute. That is restricted to incompressible (0-Mach-number, or perhaps less paradoxically, negligible-Mach-number, since strictly speaking M = 0 means "no motion") flow, thus consists of the vector momentum equation supplemented by mass conservation, which in incompressible form simply amounts to divergence-free-ness of the velocity field. Most crucially, assuming incompressibility means throwing out the energy conservation equation, which is needed to close the system when M != 0 or there are thermal phenomena (e.g. temperature gradients) and one is actually properly modeling energy conversion (between the internal and kinetic forms) and dissipation via heat transfer, which prevents actual energy-singularities from forming in the real world.

Thus, to talk about the possibility of "infinite energy density" when one has tossed the first law of thermodynamics overboard is, in relation to actual physics and real-world fluid phenomena, sheer nonsense.

The real irony is that in excluding compressible-flow phenomena, the problem posers and prize-seekers have excluded the whole host of fluid-dynamic phenomena which do in fact show behavior that is "as nearly singular as nature allows". Chiefly I mean shock waves, for which the singularity is not in the form of oo energy density but in the form of a jump discontinuity in velocity, pressure and temperature. [Riemann studied a 1-d version of this via the now-named-thusly shock tube or Riemann problem.] Perhaps the math-issue here is that the true 'jump' singularity is for the inviscid compressible N-S, a.k.a. Euler equations, but even in the real world, in the presence of viscosity and with the continuum assumption breaking down at microscopic scales, actual measurements of shock wave structure show a thickness of only a few molecular mean free paths.

While part of the Times article is quite pretty, they are definitely on thin ice in my book regarding objectivity and responsible journalism.

This is a better explanation of the particular thinking that Terry Tao is considering WRT Navier-Stokes:

Finite time blowup for an averaged three-dimensional Navier-Stokes equation
Terence Tao
(Submitted on 3 Feb 2014 (v1), last revised 1 Apr 2015 (this version, v3))
[url]http://arxiv.org/abs/1402.0290v3[/url]
(I haven't looked at the paper)

and

[URL="https://www.quantamagazine.org/20140224-a-fluid-new-path-in-grand-math-challenge/"]A Fluid New Path in Grand Math Challenge[/URL]
[QUOTE]"It’s a very fanciful idea, and I don’t expect this program to come to fruition any time in the next five years,” Tao said. Nevertheless, he said, it may be possible to harness fluid effects such as miniature vortex sheets to create water barriers that could serve as pipes.

The new proposal, however intriguing, is just speculation, cautioned Peter Constantin of Princeton University. “This is mathematics,” he said. “What’s proved is proved.”

Tao’s ideas certainly aren’t standard, Friedlander said. “But results about global regularity, whether positive or negative, will almost certainly require something that is nonstandard.” Tao’s ideas are quite likely to lead to some interesting mathematics, she said, whether or not they answer the Navier-Stokes question.

Meanwhile, Tao’s new program for tackling Navier-Stokes has changed his thinking about the problem. Previously, he had viewed both sides of the problem — proving global regularity or establishing that solutions can blow up — as equally remote goals (though in the end, only one can be true). Now he believes that it should be possible to concoct special scenarios in which a solution to the Navier-Stokes equations blows up. (This wouldn’t mean that the real ocean could blow up — instead, it would suggest that in these rare cases, the Navier-Stokes equations don’t fully capture the ocean’s physics.) “My mindset has certainly changed,” he said.

A central insight of computer science is that, whenever a physical phenomenon is complex enough, it should be possible to use it to build a universal computer — one capable of doing anything computers can do, including building self-replicating machines.

“Can you make fancy patterns of water that actually have some computation power?” Tao asked. “I’m betting that fluids are complex enough to do this.”[/QUOTE]

[url=discovermagazine.com/2015/june/23-making-a-mark]Who Were the World's First Artists?[/url] | DiscoverMagazine.com

[url=www.nature.com/news/neanderthals-had-outsize-effect-on-human-biology-1.18086?WT.mc_id=TWT_NatureNews]Neanderthals had outsize effect on human biology[/url] : Nature News & Comment (Time to break out the [i]Quest For Fire[/i] DVD...)

[URL="http://www.geek.com/science/cellulose-paper-could-be-strong-enough-to-replace-metal-1629807/"]Cellulose paper could be strong enough to replace metal[/URL]
[QUOTE]They began their study by developing sheets of paper made of cellulose — a renewable, plant-based resource. They made these papers with varying sizes of cellulose fibers, ranging in 30 micrometers to 10 nanometers — all sizes too small to see with the naked eye. They found that the paper made of 10-nanometer thick fibers was 40 times tougher and 130 times stronger than standard notebook paper, which contains cellulose fibers a thousand times larger.

What makes these smaller cellulose fibers so much stronger and tougher than most materials lie within its hydrogen bonds. Cellulose chains are linked by hydrogen bonds, and when the cellulose is broken, the bonds can reform all by themselves, giving the material a “self-healing” quality. In addition, the smaller cellulose fibers means there are more hydrogen bonds per square area, compared to larger fibers, which leads to a stronger, tougher material that can reform more quickly.[/QUOTE]

[URL="http://www.nature.com/nature/journal/v524/n7563/full/524008b.html"]Only left-handed particles decay[/URL] (paywalled)
Nature 524, 8 (06 August 2015) doi:10.1038/524008b
Published online 05 August 2015

[URL="http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/newssummary/news_27-7-2015-10-41-30"]New study shows universe is left-handed[/URL] Imperial College London by Laura Gallagher (27 July 2015)
[QUOTE]The lambda b baryon decays into different particles – a proton, a muon and a neutrino. Within the lambda b are even smaller elements, called quarks. The researchers were interested to see how one particular quark, called the beauty, or b quark, decayed into another type of quark, called an up quark.

The measurements taken by the team, published today in Nature Physics, demonstrated that the decay only takes place when the beauty quark has a ‘left-handed’ spin.

“Our results show that the decay does indeed behave in a left-handed way. The ‘handedness’ of the universe is, in combination with differences between matter and antimatter, fundamental for how our universe evolved,” says Professor Ulrik Egede, from the Department of Physics at Imperial College London. “Because the weak force is the only one of the fundamental forces to distinguish between right and left, we can also say that the Universe has a left-handed bias.”

“Although this left-handedness is predicted by the widely accepted Standard Model of physics, it has also been refuted by some physicists in recent years,” adds Professor Egede,. “We now need to explore other decays to understand why past measurements gave inconsistent results with a purely left-handed decay.”

The team is working within the Large Hadron Collider Beauty experiment (LHCb) which is funded in the UK mainly by the Science and Technology Facilities Council. Its purpose is to investigate the nature and behaviour of beauty quarks and use these observations to try to shed light on some of the universe’s biggest mysteries, including the nature of dark matter.

Scientists had previously suggested that if right-handed quarks were participating in the decay as well, this might indicate that other forces are at work in the universe, besides the four – gravity, electromagnetism, weak and strong nuclear – described in the Standard Model. Investigation of these other forces could yield important clues about dark matter.

This study is important because it shows that any new fundamental force with a right-handed component is not involved in the decay – a setback for physicists searching for these new forces.[/QUOTE]