Nosimpler

Another year has passed and Vera Rubin was not awarded the Nobel Prize. She’s 88 and the prize can’t be awarded posthumously, so I can’t shake the impression the Royal Academy is waiting for her to die while they work off a backlog of condensed-matter breakthroughs. Sure, nobody knows whether galaxies actually contain the weakly interacting and non-luminous particles we have come to call dark

Perhaps stop calling them self-driving then?

Uber provided ride-alongs to reporters on Tuesday. During a ride of about one hour, Reuters observed the Uber car safely - and for the most part smoothly - stop at red lights and accelerate at green lights, travel over a bridge, move around a mail truck and slow for a driver opening a car door on a busy street. All without a person touching the controls.

But the Uber driver and the engineer in the front two seats did intervene every few miles.

The technology is neat, but unless you get to 100% it just isn't more than neat, and it certainly won't do a damn thing for car services like Uber. Segways are neat, too.

Neural Computation, Volume 28, Issue 11, Page 2533-2556, November 2016.

And fully functional.

New York’s Guggenheim museum unveiled its latest installation on Friday – a solid gold toilet titled America.

The toilet, which the Guardian can confirm is fully functioning, is the work of Italian artist Maurizio Cattelan...

Visitors to the museum are able to use the golden toilet in much the same way as they would use a normal toilet. It is located in a standard, pre-existing bathroom on the fourth floor of the museum, a small placard the only indication of its presence...

Nathan Otterson, senior conservator, objects at the Guggenheim, is responsible for maintaining the toilet. He said a cleaning crew will attend to the toilet every 15 minutes... “We would hope no one would try to remove part of the toilet,” Otterson said. 

Image cropped for size from the original (credit William Edwards/AFP/Getty Images).

I spent the early afternoon consulting with the Evil League of Evil Labor Economists, and here were their suggestions for how to attract workers if you're having some trouble doing so.

a) Offer a higher wage. Yes, yes, wages, are so 20th century, but The Kids Today have a strange affinity for them. Maybe it's nostalgia. They even want dollars, and not Bitcoins or Applebucks.

b) Good health insurance. Weirdly, even though President Kenyan Muslim Socialist nationalized the health care industry, some Kids Today just aren't happy with their death panels and want their companies to buy redundant policies for them. Silly Kids Today.

c) Retirement benefits. Yes, yes, they've been watching too many old movies. Silent movies, starring Steve Simels mostly. But The Kids Today have these romantic notions that come retirement they won't have to do a Logan's Run or face their prescribed destiny. They've been told their whole lives that Social Security just won't be there for them so they need an alternative. Blame whoever keeps telling them that (shhh!!!!).

d) On the job training. It's true The Kids Today don't major in anything useful, unlike the Greatest Generation and the Second Greatest Generation and the Pretty Good Generation After That who all had degrees in Physics or Engineering before going on to work in opinion journalism, but that's the labor force you have to deal with. Might have to show them a thing or two.

e) Job Security. The Kids Today would like some assurances that their jobs might be around a few months hence. Yes that goes against everything the Washington Post opinion page has been telling you. Tenure of any kind is anathema to them. The job turnover there is brutal. It seems that every 20 or 30 years or so there's a new columnist!

It's going to take a lot to lure them from their parents' basements. But, sadly, that pesky 13th Amendment was ratified, or so they claim, so if you want The Kids Today to come work for you, sacrifices must be made.

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation may split into an initial exponential decrease, characterized by the maximal Lyapunov exponent, and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. The time scales of both processes can be either of the same or of very different orders of magnitude. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and therefore remain partially predictable.

Tests for distinguishing chaos from laminar flow widely use the time evolution of inter-orbital correlations as an indicator. Standard tests however yield mostly ambiguous results when it comes to distinguish partially predictable chaos and laminar flow, which are characterized respectively by attractors of fractally broadened braids and limit cycles. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories, showing that this test robustly discriminates chaos, including partially predictable chaos, from laminar flow. One can use furthermore the finite time cross-correlation of pairs of initially close trajectories to distinguish, for a complete classification, also between strong and partially predictable chaos. We are thus able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

Humans are highly sensitive to symmetry. During scene exploration, the area of the retina with dense light receptor coverage acquires most information from relevant locations determined by gaze fixation. We characterized patterns of fixational eye movements made by observers staring at synthetic scenes either freely (i.e., free exploration) or during a symmetry orientation discrimination task (i.e., active exploration). Stimuli could be mirror-symmetric or not. Both free and active exploration generated more saccades parallel to the axis of symmetry than along other orientations. Most saccades were small (<2°), leaving the fovea within a 4° radius of fixation. Analysis of saccade dynamics showed that the observed parallel orientation selectivity emerged within 500 ms of stimulus onset and persisted throughout the trials under both viewing conditions. Symmetry strongly distorted existing anisotropies in gaze direction in a seemingly automatic process. We argue that this bias serves a functional role in which adjusted scene sampling enhances and maintains sustained sensitivity to local spatial correlations arising from symmetry.

Is spacetime really a continuum? That is, can points of spacetime really be described—at least locally—by lists of four real numbers ? Or is this description, though immensely successful so far, just an approximation that breaks down at short distances?

Rather than trying to answer this hard question, let’s look back at the struggles with the continuum that mathematicians and physicists have had so far.

The worries go back at least to Zeno. Among other things, he argued that that an arrow can never reach its target:

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.—Aristotle summarizing Zeno

and Achilles can never catch up with a tortoise:

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.—Aristotle summarizing Zeno

These paradoxes can now be dismissed using our theory of real numbers. An interval of finite length can contain infinitely many points. In particular, a sum of infinitely many terms can still converge to a finite answer.

But the theory of real numbers is far from trivial. It became fully rigorous only considerably after the rise of Newtonian physics. At first, the practical tools of calculus seemed to require infinitesimals, which seemed logically suspect. Thanks to the work of Dedekind, Cauchy, Weierstrass, Cantor and others, a beautiful formalism was developed to handle real numbers, limits, and the concept of infinity in a precise axiomatic manner.

However, the logical problems are not gone. Gödel’s theorems hang like a dark cloud over the axioms of mathematics, assuring us that any consistent theory as strong as Peano arithmetic, or stronger, cannot prove itself consistent. Worse, it will leave some questions unsettled.

For example: how many real numbers are there? The continuum hypothesis proposes a conservative answer, but the usual axioms of set theory leaves this question open: there could vastly more real numbers than most people think. And the superficially plausible axiom of choice—which amounts to saying that the product of any collection of nonempty sets is nonempty—has scary consequences, like the existence of non-measurable subsets of the real line. This in turn leads to results like that of Banach and Tarski: one can partition a ball of unit radius into six disjoint subsets, and by rigid motions reassemble these subsets into two disjoint balls of unit radius. (Later it was shown that one can do the job with five, but no fewer.)

However, most mathematicians and physicists are inured to these logical problems. Few of us bother to learn about attempts to tackle them head-on, such as:

• nonstandard analysis and synthetic differential geometry, which let us work consistently with infinitesimals,

• constructivism, which avoids proof by contradiction: for example, one must ‘construct’ a mathematical object to prove that it exists,

• finitism (which avoids infinities altogether),

• ultrafinitism, which even denies the existence of very large numbers.

This sort of foundational work proceeds slowly, and is now deeply unfashionable. One reason is that it rarely seems to intrude in ‘real life’ (whatever that is). For example, it seems that no question about the experimental consequences of physical theories has an answer that depends on whether or not we assume the continuum hypothesis or the axiom of choice.

But even if we take a hard-headed practical attitude and leave logic to the logicians, our struggles with the continuum are not over. In fact, the infinitely divisible nature of the real line—the existence of arbitrarily small real numbers—is a serious challenge to almost all of the most widely used theories of physics.

Indeed, we have been unable to rigorously prove that most of these theories make sensible predictions in all circumstances, thanks to problems involving the continuum.

One might hope that a radical approach to the foundations of mathematics—such as those listed above—would allow avoid some of the problems I’ll be discussing. However, I know of no progress along these lines that would interest most physicists. Some of the ideas of constructivism have been embraced by topos theory, which also provides a foundation for calculus with infinitesimals using synthetic differential geometry. Topos theory and especially higher topos theory are becoming important in mathematical physics. They’re great! But as far as I know, they have not been used to solve the problems I want to discuss here.

Today I’ll talk about one of the first theories to use calculus: Newton’s theory of gravity.

Newtonian Gravity

In its simplest form, Newtonian gravity describes ideal point particles attracting each other with a force inversely proportional to the square of their distance. It is one of the early triumphs of modern physics. But what happens when these particles collide? Apparently the force between them becomes infinite. What does Newtonian gravity predict then?

Of course real planets are not points: when two planets come too close together, this idealization breaks down. Yet if we wish to study Newtonian gravity as a mathematical theory, we should consider this case. Part of working with a continuum is successfully dealing with such issues.

In fact, there is a well-defined ‘best way’ to continue the motion of two point masses through a collision. Their velocity becomes infinite at the moment of collision but is finite before and after. The total energy, momentum and angular momentum are unchanged by this event. So, a 2-body collision is not a serious problem. But what about a simultaneous collision of 3 or more bodies? This seems more difficult.

Worse than that, Xia proved in 1992 that with 5 or more particles, there are solutions where particles shoot off to infinity in a finite amount of time!

This sounds crazy at first, but it works like this: a pair of heavy particles orbit each other, another pair of heavy particles orbit each other, and these pairs toss a lighter particle back and forth. Xia and Saari’s nice expository article has a picture of the setup:

Each time the lighter particle gets thrown back and forth, the pairs move further apart from each other, while the two particles within each pair get closer together. And each time they toss the lighter particle back and forth, the two pairs move away from each other faster!

As the time approaches a certain value the speed of these pairs approaches infinity, so they shoot off to infinity in opposite directions in a finite amount of time, and the lighter particle bounces back and forth an infinite number of times!

Of course this crazy behavior isn’t possible in the real world, but Newtonian physics has no ‘speed limit’, and we’re idealizing the particles as points. So, if two or more of them get arbitrarily close to each other, the potential energy they liberate can give some particles enough kinetic energy to zip off to infinity in a finite amount of time! After that time, the solution is undefined.

You can think of this as a modern reincarnation of Zeno’s paradox. Suppose you take a coin and put it heads up. Flip it over after 1/2 a second, then flip it over after 1/4 of a second, and so on. After one second, which side will be up? There is no well-defined answer. That may not bother us, since this is a contrived scenario that seems physically impossible. It’s a bit more bothersome that Newtonian gravity doesn’t tell us what happens to our particles when

Your might argue that collisions and these more exotic ‘noncollision singularities’ occur with probability zero, because they require finely tuned initial conditions. If so, perhaps we can safely ignore them!

This is a nice fallback position. But to a mathematician, this argument demands proof.

A bit more precisely, we would like to prove that the set of initial conditions for which two or more particles come arbitrarily close to each other within a finite time has ‘measure zero’. This would mean that ‘almost all’ solutions are well-defined for all times, in a very precise sense.

In 1977, Saari proved that this is true for 4 or fewer particles. However, to the best of my knowledge, the problem remains open for 5 or more particles. Thanks to previous work by Saari, we know that the set of initial conditions that lead to collisions has measure zero, regardless of the number of particles. So, the remaining problem is to prove that noncollision singularities occur with probability zero.

It is remarkable that even Newtonian gravity, often considered a prime example of determinism in physics, has not been proved to make definite predictions, not even ‘almost always’! In 1840, Laplace wrote:

We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence.—Laplace

However, this dream has not yet been realized for Newtonian gravity.

I expect that noncollision singularities will be proved to occur with probability zero. If so, the remaining question would why it takes so much work to prove this, and thus prove that Newtonian gravity makes definite predictions in almost all cases. Is this is a weakness in the theory, or just the way things go? Clearly it has something to do with three idealizations:

• point particles whose distance can be arbitrarily small,

• potential energies that can be arbitrariy large and negative,

• velocities that can be arbitrarily large.

These are connected: as the distance between point particles approaches zero, their potential energy approaches and conservation of energy dictates that some velocities approach

Does the situation improve when we go to more sophisticated theories? For example, does the ‘speed limit’ imposed by special relativity help the situation? Or might quantum mechanics help, since it describes particles as ‘probability clouds’, and puts limits on how accurately we can simultaneously know both their position and momentum?

Next time I’ll talk about quantum mechanics, which indeed does help.

Nature Neuroscience 19, 1192 (2016). doi:10.1038/nn.4369

Authors: Stanislas Dehaene & Ghislaine Dehaene-Lambertz

Even before a child learns to read, the future location of his or her letter-processing area can be predicted from its connections to the rest of the brain. Reading acquisition thus piggybacks on a pre-existing brain circuit.

Looking at my list of items to blog about, I see most of them have some relation to the Templeton Foundation, so this will be a blog post just about those. To get some idea of the scale of Templeton’s activities, at the end of 2014 they had about $3.2 billion in assets, and during 2014 had given away about $185 million. For comparison, the NSF budget for FY2014 for physics was $267 million and for mathematics $225 million.

One of the main goals of the foundation is to bring together science and religion. Among the many things they are funding to accomplish this is a $871,000 grant to Arizona State University to fund Think Write Publish Fellowships in Science and Religion. If you’re a hard-up writer, these people will give you the opportunity to get $10,000 to write “creative nonfiction stories about harmonies between science and religion” and help you get them published.

Over the next few years, as you see things like this make it into the media, realize that this is not evidence of an intellectual trend, but a reflection of Templeton money and their agenda. ASU’s Lawrence Krauss is, for good reason, not happy.

To give an idea of the range of Templeton’s influence, just at ASU they’re funding several other large grants, including $745,000 for Representations of God (this and this), and $544,000 for emergent gravity. When you notice conferences, seminars, public lectures, etc. about “emergent gravity” in coming years, realize that some of them are happening because of Templeton’s agenda (one of the PIs is a Templeton Prize winner).

One of Templeton’s largest recent grants has been $4.7 million to FQXI for research into “Physics of the Observer”. Among other things, this funded a recent conference at Banff.

A major interest of Templeton’s over the years has been “Genius”. Another of their large recent grants has been to the World Science Foundation for its Cultivating Genius Initiative.

Finally, there will be an interesting mathematics conference related to quantum field theory at Harvard October 8-10. I’ll likely be up in Boston visiting my brother and hope to maybe attend some of the talks. Funding for this is coming partially from the “Templeton Charity Foundation Switzerland”. I guess this is these people, some off-shoot of the Templeton Foundation, with exactly the same interests, They say they have made $85.2 million in grants, a list is here.

Update: I was thinking of commenting that Templeton at least seemed to have slowed down its efforts to promote multiverse mania. But then I noticed this. If you want to know why Ira Flatow on NPR keeps bringing up the multiverse, $150,000 in Templeton money might have something to do with it…

Update: I keep on finding out about more of these Templeton-funded things, they are endless. Templeton is funding an Institute for Cross-Disciplinary Engagement at Dartmouth. Themes to be investigated are “Can science alone explain the nature of reality?”, “Is there free will?” and “Is there purpose in the universe?”. Among their many activities will be an event featuring a dialogue between Sean Carroll and a Buddhist Scholar in San Francisco in February.

NEW YORK (Reuters) - A judge on Thursday rejected Citigroup Inc's bid for a preliminary injunction to stop AT&T Inc from using the phrase "AT&T thanks" on a customer loyalty program, which the bank called too similar to its trademarked "thankyou."

U.S. District Judge Katherine Forrest in Manhattan said Citigroup has not shown that customers would likely be confused, or that it would suffer irreparable harm, if AT&T kept saying "AT&T thanks" while the bank's lawsuit continued.

She also said AT&T provided solid evidence that forcing it to start saying something other than "AT&T thanks" would cause an "expensive and significant disruption."

Citigroup had no immediate comment. AT&T said in a statement it was pleased with the decision, and maintained that "the law does not allow one company to own the word 'thanks.'"

The fourth-largest U.S. bank by assets sued AT&T on June 9, one week after the Dallas-based phone company launched "AT&T thanks" in a dispute that threatened to damage a co-branding relationship dating to 1998.

Citigroup said AT&T went too far, having known it would object after the New York-based bank had since 2004 extensively used "thankyou" on its own customer loyalty and reward programs.

Offered without comment.

The company that makes EpiPens has decided to gouge the hell out of people. There's nothing magical about the drugs. They're cheap and off patent. It's the delivery device. No one's having any luck getting a quality competitor past the FDA.

Will this crisis be solved? It probably depends on how many members of Congress have family members who need them.

My daughter has severe allergies. I've seen firsthand that EpiPens are lifesavers & I'm pressing for answers https://t.co/kOJym0gvdV

— Mark Warner (@MarkWarner) August 23, 2016

Because that's how things work. Oh, and the CEO of the company that makes them just happens to be the daughter of another US senator. Because that's how things work, too.

I’m revising the notes for the introductory linear algebra class that I teach, and wondering whether I can find a way to fit in the wonderful but curiously unpromoted Gershgorin disc theorem.

The Gershgorin disc theorem is an elementary result that allows you to make very fast deductions about the locations of eigenvalues. For instance, it lets you look at the matrix

(3 i 1 −1 4+5i 2 2 1 −1) \begin{pmatrix} 3 &i &1 \\ -1 &4 + 5i &2 \\ 2 &1 &-1 \end{pmatrix}

and see, with only the most trivial mental arithmetic, that the real parts of its eigenvalues must all lie between −4-4 and 77 and the imaginary parts must lie between −3-3 and 88.

I wasn’t taught this theorem as an undergraduate, and ever since I learned it a few years ago, have wondered why not. I feel ever so slightly resentful about it. The theorem is so useful, and the proof is a pushover. Was it just me? Did you get taught the Gershgorin disc theorem as an undergraduate?

Here’s the statement:

Theorem (Gershgorin) Let A=(a ij)A = (a_{i j}) be a square complex matrix. Then every eigenvalue of AA lies in one of the Gershgorin discs

{z∈ℂ:|z−a ii|≤r i} \{ z \in \mathbb{C} \colon |z - a_{i i}| \leq r_i \}

where r i=∑ j≠i|a ij|r_i = \sum_{j \neq i} |a_{i j}|.

For example, if

A=(3 i 1 −1 4+5i 2 2 1 −1) A = \begin{pmatrix} 3 &i &1 \\ -1 &4 + 5i &2 \\ 2 &1 &-1 \end{pmatrix}

(as above) then the three Gershgorin discs have:

• centre 33 and radius |i|+|1|=2|i| + |1| = 2,
• centre 4+5i4 + 5i and radius |−1|+|2|=3|-1| + |2| = 3,
• centre −1-1 and radius |2|+|1|=3|2| + |1| = 3.

Gershgorin’s theorem says that every eigenvalue lies in the union of these three discs. My statement about real and imaginary parts follows immediately.

Even the proof is pathetically simple. Let λ\lambda be an eigenvalue of AA. Choose a λ\lambda-eigenvector xx, and choose ii so that |x i||x_i| is maximized. Taking the iith coordinate of the equation Ax=λxA x = \lambda x gives

(λ−a ii)x i=∑ j≠ia ijx j. (\lambda - a_{i i})x_i = \sum_{j \neq i} a_{i j} x_j.

Now take the modulus of each side:

|λ−a ii||x i|=|∑ j≠ia ijx j|≤∑ j≠i|a ij||x j|≤(∑ j≠i|a ij|)|x i|=r i|x i| |\lambda - a_{i i}| |x_i| = \left| \sum_{j \neq i} a_{i j} x_j \right| \leq \sum_{j \neq i} |a_{i j}| |x_j| \leq \left( \sum_{j \neq i} |a_{i j}| \right) |x_i| = r_i |x_i|

where to get the inequalities, we used the triangle inequality and then the maximal property of |x i||x_i|. Cancelling |x i||x_i| gives |λ−a ii|≤r i|\lambda - a_{i i}| \leq r_i. And that’s it!

The theorem is often stated with a supplementary part that gives further information about the location of the eigenvalues: if the union of kk of the discs forms a connected-component of the union of all of them, then exactly kk eigenvalues lie within it. In the example shown, this tells us that there’s exactly one eigenvalue in the blue disc at the top right and exactly two eigenvalues in the union of the red and green discs. (But the theorem says nothing about where those two eigenvalues are within that union.) That’s harder to prove, so I can understand why it wouldn’t be taught in a first course.

But the main part is entirely elementary in both its statement and its proof, as well as being immediately useful. As far as that main part is concerned, I’m curious to know: when did you first meet Gershgorin’s disc theorem?

Yo, everyone! The final version of my book now exists, and I have exactly one copy! Here’s my editor, Amanda Cook, holding it yesterday when we met for beers:

Here’s my son holding it:

Here’s the back of the book, with blurbs from really exceptional people:

In other exciting book news, there’s a review by Richard Beales from Reuter’s BreakingViews, and it made a list of new releases in Scientific American as well.

Endnote:

I want to apologize in advance for all the book news I’m going to be blogging, tweeting, and otherwise blabbing about. To be clear, I’ve been told it’s my job for the next few months to be a PR person for my book, so I guess that’s what I’m up to. If you come here for ideas and are turned off by cheerleading, feel free to temporarily hate me, and even unsubscribe to whatever feed I’m in for you!

But please buy my book first, available for pre-order now. And feel free to leave an amazing review.

Author(s): Mark Buchanan

Experiments confirm the existence of 1-micrometer-sized molecules made of two cesium atoms by showing that their binding energies agree with predictions.  

[Physics 9, 99] Published Fri Aug 19, 2016

Merriam-Webster's Word of the Day for July 30, 2016 is:

littoral • \LIT-uh-rul\  • adjective

: of, relating to, or situated or growing on or near a shore especially of the sea

Examples:

The report shows dramatic improvement in the condition of the state's littoral waters since the cleanup effort began.

"But this project will permanently add new sand to the beach and dune system of Dauphin Island's East End, and the new sand will stay in the littoral system for centuries." — Scott Douglass, The Mobile (Alabama) Register, 6 Mar. 2016

Did you know?

You're most likely to encounter littoral in contexts relating to the military and marine sciences. A littoral combat ship is a fast and easily maneuverable combat ship built for use in coastal waters. And in marine ecology, the littoral zone is a coastal zone characterized by abundant dissolved oxygen, sunlight, nutrients, and generally high wave energies and water motion. Littoral can also be found as a noun referring to a coastal region or, more technically, to the shore zone between the high tide and low tide points. The adjective is the older of the two, dating from the mid-17th century; the noun dates from the early 19th century. The word comes to English from Latin litoralis, itself from litor- or litus, meaning "seashore."

Sometimes the ones from Virginia can surprise.

“Once again, the Virginia Supreme Court has placed Virginia as an outlier in the struggle for civil and human rights. It is a disgrace that the Republican leadership of Virginia would file a lawsuit to deny more than 200,000 of their own citizens the right to vote. And I cannot accept that this overtly political action could succeed in suppressing the voices of many thousands of men and women who had rejoiced with their families earlier this year when their rights were restored.

“Forty states give citizens who have made mistakes and paid their debt to society a straightforward process for restoring voting rights. I remain committed to moving past our Commonwealth’s history of injustice to embrace an honest process for restoring the rights of our citizens, and I believe history and the vast majority of Virginians are on our side.

“Despite the Court’s ruling, we have the support of the state’s four leading constitutional experts, including A.E. Dick Howard, who drafted the current Virginia Constitution. They are convinced that our action is within the constitutional authority granted to the Office of the Governor.

“The men and women whose voting rights were restored by my executive action should not be alarmed. I will expeditiously sign nearly 13,000 individual orders to restore the fundamental rights of the citizens who have had their rights restored and registered to vote. And I will continue to sign orders until I have completed restoration for all 200,000 Virginians. My faith remains strong in all of our citizens to choose their leaders, and I am prepared to back up that faith with my executive pen. The struggle for civil rights has always been a long and difficult one, but the fight goes on.”

The celebrated medical-research reformer has a new paper (sent to me by Keith O’Rourke; official published version here), where he writes:

As EBM [evidence-based medicine] became more influential, it was also hijacked to serve agendas different from what it originally aimed for. Influential randomized trials are largely done by and for the benefit of the industry. Meta-analyses and guidelines have become a factory, mostly also serving vested interests. National and federal research funds are funneled almost exclusively to research with little relevance to health outcomes. We have supported the growth of principal investigators who excel primarily as managers absorbing more money.

He continues:

Diagnosis and prognosis research and efforts to individualize treatment have fueled recurrent spurious promises. Risk factor epidemiology has excelled in salami-sliced data-dredged papers with gift authorship and has become adept to dictating policy from spurious evidence. Under market pressure, clinical medicine has been transformed to finance-based medicine. In many places, medicine and health care are wasting societal resources and becoming a threat to human well-being. Science denialism and quacks are also flourishing and leading more people astray in their life choices, including health.

And concludes:

EBM still remains an unmet goal, worthy to be attained.

Read the whole damn thing.

The post Ioannidis: “Evidence-Based Medicine Has Been Hijacked” appeared first on Statistical Modeling, Causal Inference, and Social Science.

The post Do we need IRBs for IRBs? And should they be for-profit? appeared first on Marginal REVOLUTION.

I pass on the initial paragraphs of Douthat's excellent Op-Ed piece in Sunday's NYTimes. It it well worth a read:

NOW that populist rebellions are taking Britain out of the European Union and the Republican Party out of contention for the presidency, perhaps we should speak no more of left and right, liberals and conservatives. From now on the great political battles will be fought between nationalists and internationalists, nativists and globalists. From now on the loyalties that matter will be narrowly tribal — Make America Great Again, this blessed plot, this earth, this realm, this England — or multicultural and cosmopolitan.

Well, maybe. But describing the division this way has one great flaw. It gives the elite side of the debate (the side that does most of the describing) too much credit for being truly cosmopolitan.

Genuine cosmopolitanism is a rare thing. It requires comfort with real difference, with forms of life that are truly exotic relative to one’s own. It takes its cue from a Roman playwright’s line that “nothing human is alien to me,” and goes outward ready to be transformed by what it finds.

The people who consider themselves “cosmopolitan” in today’s West, by contrast, are part of a meritocratic order that transforms difference into similarity, by plucking the best and brightest from everywhere and homogenizing them into the peculiar species that we call “global citizens.”

This species is racially diverse (within limits) and eager to assimilate the fun-seeming bits of foreign cultures — food, a touch of exotic spirituality. But no less than Brexit-voting Cornish villagers, our global citizens think and act as members of a tribe.

They have their own distinctive worldview (basically liberal Christianity without Christ), their own common educational experience, their own shared values and assumptions (social psychologists call these WEIRD — for Western, Educated, Industrialized, Rich and Democratic), and of course their own outgroups (evangelicals, Little Englanders) to fear, pity and despise. And like any tribal cohort they seek comfort and familiarity: From London to Paris to New York, each Western “global city” (like each “global university”) is increasingly interchangeable, so that wherever the citizen of the world travels he already feels at home.

The ending lines:

They can’t see that paeans to multicultural openness can sound like self-serving cant coming from open-borders Londoners who love Afghan restaurants but would never live near an immigrant housing project, or American liberals who hail the end of whiteness while doing everything possible to keep their kids out of majority-minority schools.

They can’t see that their vision of history’s arc bending inexorably away from tribe and creed and nation-state looks to outsiders like something familiar from eras past: A powerful caste’s self-serving explanation for why it alone deserves to rule the world.

Naturalness, according to physicists.

Before the LHC turned on, theoretical physicists had high hopes the collisions would reveal new physics besides the Higgs. The chances of that happening get smaller by the day. The possibility still exists, but the absence of new physics so far has already taught us an important lesson: Nature isn’t natural. At least not according to theoretical physicists.

The reason that many in the community expected new physics at the LHC was the criterion of naturalness. Naturalness, in general, is the requirement that a theory should not contain dimensionless numbers that are either very large or very small. If that is so, then theorists will complain the numbers are “finetuned” and regard the theory as contrived and hand-made, not to say ugly.

Technical naturalness (originally proposed by ‘t Hooft) is a formalized version of naturalness which is applied in the context of effective field theories in particular. Since you can convert any number much larger than one into a number much smaller than one by taking its inverse, it’s sufficient to consider small numbers in the following. A theory is technically natural if all suspiciously small numbers are protected by a symmetry. The standard model is technically natural, except for the mass of the Higgs.

The Higgs is the only (fundamental) scalar we know and, unlike all the other particles, its mass receives quantum corrections of the order of the cutoff of the theory. The cutoff is assumed to be close by the Planck energy – that means the estimated mass is 15 orders of magnitude larger than the observed mass. This too-large mass of the Higgs could be remedied simply by subtracting a similarly large term. This term however would have to be delicately chosen so that it almost, but not exactly, cancels the huge Planck-scale contribution. It would hence require finetuning.

In the framework of effective field theories, a theory that is not natural is one that requires a lot of finetuning at high energies to get the theory at low energies to work out correctly. The degree of finetuning can, and has been, quantified in various measures of naturalness. Finetuning is thought of as unacceptable because the theory at high energy is presumed to be more fundamental. The physics we find at low energies, so the argument, should not be highly sensitive to the choice we make for that more fundamental theory.

Until a few years ago, most high energy particle theorists therefore would have told you that the apparent need to finetuning the Higgs mass means that new physics must appear nearby the energy scale where the Higgs will be produced. The new physics, for example supersymmetry, would avoid the finetuning.

There’s a standard tale they have about the use of naturalness arguments, which goes somewhat like this:

1) The electron mass isn’t natural in classical electrodynamics, and if one wants to avoid finetuning this means new physics has to appear at around 70 MeV. Indeed, new physics appears even earlier in form of the positron, rendering the electron mass technically natural.

2) The difference between the masses of the neutral and charged pion is not natural because it’s suspiciously small. To prevent fine-tuning one estimates new physics must appear around 700 MeV, and indeed it shows up in form of the rho meson.

3) The lack of flavor changing neutral currents in the standard model means that a parameter which could a priori have been anything must be very small. To avoid fine-tuning, the existence of the charm quark is required. And indeed, the charm quark shows up in the estimated energy range.

From these three examples only the last one was an actual prediction (Glashow, Iliopoulos, and Maiani, 1970). To my knowledge this is the only prediction that technical naturalness has ever given rise to – the other two examples are post-dictions.

Not exactly a great score card.

But well, given that the standard model – in hindsight – obeys this principle, it seems reasonable enough to extrapolate it to the Higgs mass. Or does it? Seeing that the cosmological constant, the only other known example where the Planck mass comes in, isn’t natural either, I am not very convinced.

A much larger problem with naturalness is that it’s a circular argument and thus a merely aesthetic criterion. Or, if you prefer, a philosophic criterion. You cannot make a statement about the likeliness of an occurrence without a probability distribution. And that distribution already necessitates a choice.

In the currently used naturalness arguments, the probability distribution is assumed to be uniform (or at least approximately uniform) in a range that can be normalized to one by dividing through suitable powers of the cutoff. Any other type of distribution, say, one that is sharply peaked around small values, would require the introduction of such a small value in the distribution already. But such a small value justifies itself by the probability distribution just like a number close to one justifies itself by its probability distribution.

Naturalness, hence, becomes a chicken-and-egg problem: Put in the number one, get out the number one. Put in 0.00004, get out 0.00004. The only way to break that circle is to just postulate that some number is somehow better than all other numbers.

The number one is indeed a special number in that it’s the unit element of the multiplication group. One can try to exploit this to come up with a mechanism that prefers a uniform distribution with an approximate width of one by introducing a probability distribution on the space of probability distributions, leading to a recursion relation. But that just leaves one to explain why that mechanism.

Another way to see that this can’t solve the problem is that any such mechanism will depend on the basis in the space of functions. Eg, you could try to single out a probability distribution by asking that it’s the same as its Fourier-transformation. But the Fourier-transformation is just one of infinitely many basis transformations in the space of functions. So again, why exactly this one?

Or you could try to introduce a probability distribution on the space of transformations among bases of probability distributions, and so on. Indeed I’ve played around with this for some while. But in the end you are always left with an ambiguity, either you have to choose the distribution, or the basis, or the transformation. It’s just pushing around the bump under the carpet.

The basic reason there’s no solution to this conundrum is that you’d need another theory for the probability distribution, and that theory per assumption isn’t part of the theory for which you want the distribution. (It’s similar to the issue with the meta-law for time-varying fundamental constants, in case you’re familiar with this argument.)

In any case, whether you buy my conclusion or not, it should give you a pause that high energy theorists don’t ever address the question where the probability distribution comes from. Suppose there indeed was a UV-complete theory of everything that predicted all the parameters in the standard model. Why then would you expect the parameters to be stochastically distributed to begin with?

This lacking probability distribution, however, isn’t my main issue with naturalness. Let’s just postulate that the distribution is uniform and admit it’s an aesthetic criterion, alrighty then. My main issue with naturalness is that it’s a fundamentally nonsensical criterion.

Any theory that we can conceive of which describes nature correctly must necessarily contain hand-picked assumptions which we have chosen “just” to fit observations. If that wasn’t so, all we’d have left to pick assumptions would be mathematical consistency, and we’d end up in Tegmark’s mathematical universe. In the mathematical universe then, we’d no longer have to choose a consistent theory, ok. But we’d instead have to figure out where we are, and that’s the same question in green.

All our theories contain lots of assumptions like Hilbert-spaces and Lie-algebras and Haussdorf measures and so on. For none of these is there any explanation other than “it works.” In the space of all possible mathematics, the selection of this particular math is infinitely fine-tuned already – and it has to be, for otherwise we’d be lost again in Tegmark space.

The mere idea that we can justify the choice of assumptions for our theories in any other way than requiring them to reproduce observations is logical mush. The existing naturalness arguments single out a particular type of assumption – parameters that take on numerical values – but what’s worse about this hand-selected assumption than any other hand-selected assumption?

This is not to say that naturalness is always a useless criterion. It can be applied in cases where one knows the probability distribution, for example for the typical distances between stars or the typical quantum fluctuation in the early universe, etc. I also suspect that it is possible to find an argument for the naturalness of the standard model that does not necessitate to postulate a probability distribution, but I am not aware of one.

It’s somewhat of a mystery to me why naturalness has become so popular in theoretical high energy physics. I’m happy to see it go out of the window now. Keep your eyes open in the next couple of years and you’ll witness that turning point in the history of science when theoretical physicists stopped dictating nature what’s supposedly natural.

Occasionally I tangle with some of the "bomb everything in the name of humanitarianism" crowd. The ones who sort of know what they're talking about, in that they at least can find some of these places on the map, always ultimately justify their favorite solution to every problem by suggesting that things would be a lot worse if we didn't pour grease on the kitchen fire. The rules are that if we don't bomb enough things are our "fault." Why do you love death and economic misery, hippie? If we do bomb enough (though can you ever really bomb enough?) then things are not our fault. The ungrateful recipients of our care packages just don't understand the joy in loving freedom bombs. Actually helping people - real sustained humanitarian aid, helping refugees - is just silly hippie stuff that we couldn't possibly do. Also, you're a big racist for not wanting to bomb people.


Sometimes they go full neocon and just argue that if we don't prove that we have the biggest most frightening dick on a daily basis then the world will collapse, but mostly they're just thinking of the children and how best to help them. With our bombs.

This was a very mean post that probably hurt the feefees of those people who really just want to bomb children for their own good. That was very uncivil of me, and my tone makes me a very unserious person.

Andy Clark does a fascinating discussion and analysis of predictive processing, which turns the traditional picture of perception on its head. The embodied mind model, which seems to me completely compelling, shows the stark inadequacy of most brain centered models of mind and cognition. I pass on the end of his introduction and the closing paragraph of the essay. (This essay is just one of many on a fascinating website , Open Mind, that has posted 39 essays (edited by Thomas Metzinger and Jennifer Windt) by contributors who are both junior and senior members of the academic philosophy of mind field.

Predictive processing plausibly represents the last and most radical step in a retreat from the passive, input-dominated view of the flow of neural processing. According to this emerging class of models, naturally intelligent systems (humans and other animals) do not passively await sensory stimulation. Instead, they are constantly active, trying to predict the streams of sensory stimulation before they arrive. Before an “input” arrives on the scene, these pro-active cognitive systems are already busy predicting its most probable shape and implications. Systems like this are already (and almost constantly) poised to act, and all they need to process are any sensed deviations from the predicted state. It is these calculated deviations from predicted states (known as prediction errors) that thus bear much of the information-processing burden, informing us of what is salient and newsworthy within the dense sensory barrage. The extensive use of top-down probabilistic prediction here provides an effective means of avoiding the kinds of “representational bottleneck” feared by early opponents of representation-heavy—but feed-forward dominated—forms of processing. Instead, the downward flow of prediction now does most of the computational “heavy-lifting”, allowing moment-by-moment processing to focus only on the newsworthy departures signified by salient prediction errors. Such economy and preparedness is biologically attractive, and neatly sidesteps the many processing bottlenecks associated with more passive models of the flow of information.

Action itself...then needs to be reconceived. Action is not so much a response to an input as a neat and efficient way of selecting the next “input”, and thereby driving a rolling cycle. These hyperactive systems are constantly predicting their own upcoming states, and actively moving so as to bring some of them into being. We thus act so as to bring forth the evolving streams of sensory information that keep us viable (keeping us fed, warm, and watered) and that serve our increasingly recondite ends. PP thus implements a comprehensive reversal of the traditional (bottom-up, forward-flowing) schema. The largest contributor to ongoing neural response, if PP is correct, is the ceaseless anticipatory buzz of downwards-flowing neural prediction that drives both perception and action. Incoming sensory information is just one further factor perturbing those restless pro-active seas. Within those seas, percepts and actions emerge via a recurrent cascade of sub-personal predictions forged from unconscious expectations spanning multiple spatial and temporal scales.

Conceptually, this implies a striking reversal, in that the driving sensory signal is really just providing corrective feedback on the emerging top-down predictions. As ever-active prediction engines, these kinds of minds are not, fundamentally, in the business of solving puzzles given to them as inputs. Rather, they are in the business of keeping us one step ahead of the game, poised to act and actively eliciting the sensory flows that keep us viable and fulfilled. If this is on track, then just about every aspect of the passive forward-flowing model is false. We are not passive cognitive couch potatoes so much as proactive predictavores, forever trying to stay one step ahead of the incoming waves of sensory stimulation.

Conclusion: Towards a mature science of the embodied mind

By self-organizing around prediction error, and by learning a generative rather than a merely discriminative (i.e., pattern-classifying) model, these approaches realize many of the goals of previous work in artificial neural networks, robotics, dynamical systems theory, and classical cognitive science. They self-organize around prediction error signals, perform unsupervised learning using a multi-level architecture, and acquire a satisfying grip—courtesy of the problem decompositions enabled by their hierarchical form—upon structural relations within a domain. They do this, moreover, in ways that are firmly grounded in the patterns of sensorimotor experience that structure learning, using continuous, non-linguaform, inner encodings (probability density functions and probabilistic inference). Precision-based restructuring of patterns of effective connectivity then allow us to nest simplicity within complexity, and to make as much (or as little) use of body and world as task and context dictate. This is encouraging. It might even be that models in this broad ballpark offer us a first glimpse of the shape of a fundamental and unified science of the embodied mind.

Author(s): Benedikt Sabass and Howard A. Stone

A tiny conical deformation in a channel embedded in a lipid membrane can give rise to a significant energy release when the channel opens.

[Phys. Rev. Lett. 116, 258101] Published Mon Jun 20, 2016