by Paul North

Wind is low on the list of the awe-inspiring invisible powers. In other eras it ranked among the top forces beyond human control, blowing us this way and that. Today we think of wind as easily harnessed for human uses, as a mild amusement or nuisance, or as a fairy-tale character with puffed up cheeks and pursed lips.

If those lips could talk, we would hear some stories about uncontrollable forces. Although there hasn't been much talk of wind lately, a serious anemological investigation has been being carried out over the last three decades by the anime director Hayao Miyazaki. Wind is always blowing in Miyazaki, or almost always. Nevertheless, it doesn't always do the same thing. The main question driving his investigation into wind is: does wind liberate us or blow us in the direction of our destiny? One thing does stay steady across his films. Whatever we do on and in the wind, we never gain control over it. This doesn't mean that wind is in control of us. Miyazaki's is a control-less view of fate. Wind is the basic element in a fluid cosmic system that strews and carries, resists and supports, lifts upward and slams to earth with abandon. Where fate is King, wind is his advance scout, his highest ambassador and field marshal. It decides nothing: wind simply executes. In contrast, fate is rather abstract, a faint inkling of limits on what you can do or hope. When you face fate, however, you don't face a concept but a force. Wind is the force against which you push when you resist your fate, and when pushed, wind reveals itself to be only air. And you cannot push against air.

You can however ride it. Many things ride the wind in Miyazaki's landscapes. Pollution. War machines. Clouds. And depending how it is ridden, depending whether your calculations include the wind as the most salient factor, your endeavors may come out well or extremely ill.

In classical myths and tales wind is either a brutish force or a changeable force. The Aesop's fable about the North Wind and the Sun tells of wind's brutishness. Sun and North Wind argue: who can strip a traveler's clothes off more quickly? Wind goes first, blowing its all. Yet it doesn't loosen a button. Sun only shines on the traveler long enough and she starts to undress of her own accord. Persuasion wins over force—that's the moral of the tale. Both are forces—soft, effective persuasion and brutish, direct assault. But as a form of force, the sun is more pernicious. It disguises its violence as reason and presents its strength as gentility. Worse than this, whereas it exerts deadly force, the force appears to come from the victim—the traveler believes the decision to undress has been a free decision of her own. In contrast, the cold North Wind, Boreas, comes openly and directly, and human ingenuity can resist it, at least when it comes to clothing. Notice that both these fateful forces aim to render the traveler defenseless and naked, a plaything for nature's sadism.

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by Dave Maier

It’s been a while since my last music post, but I have to admit that the impetus for this one was less that fact, or even the release of Star Trek: Beyond, than the fact that I have not (*cough*) progressed far enough in my reading (even after finishing several more books – hey, it’s complicated!) to continue in a satisfactory manner from where I left off last time. So let’s go traveling instead (previous voyages here, here, here, here, and here).

This time: widgets! Although if you click the direct link to Mixcloud, you can access many other mixes without all the commentary.

Ashra – 77 Slightly Delayed Blackouts
Tangerine Dream – Exit Exit
Richard Pinhas – Iceland Part 2 Iceland
Eberhard Schoener – Meditation part 2 (exc.) Meditation
Jeff Greinke – Falling Away Lost Terrain
Pieter Nooten/Michael Brook – Finally II Sleeps With the Fishes
Terje Rypdal – Waves Waves
David Hykes & the Harmonic Choir – Lines to a Great Lord Harmonic Meetings

Our first mix is another time capsule from the 70s and 80s. The previous ones focused on some fairly obscure and hard-to-get material, but there’s no reason to avoid great music simply because it’s more generally available, right?

Ash Ra Tempel was one of the prime movers of the German space music scene in the early 70s, although their first efforts are more pan-stylistic lysergic freak-out – see this link for a comparison of their first album to Iggy Pop (!) – than the sequencer-driven Berlin-school material we hear later on, as in this track, the agreeably bouncy opener from 1977’s Blackouts, by which time guitarist and indeed sole member Manuel Göttsching had abridged the band name to Ashra. I love this picture, in which none of their faces is visible: drummer Klaus Schulze’s blocked by a cymbal, and Göttsching’s and bassist Hartmut Enke’s by their hair. Klaus must have liked the pic too, as he included it in the booklet of his retrospective album X in 1978, where I first saw it.

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by Humera Afridi

I arrived in Istanbul on the morning of July 3, fast on the heels of death.

Amjad Sabri, an eminent Pakistani qawwal—a Sufi devotional musician in the tradition of world-renowned Nusrat Fateh Ali Khan, and son of the famous singer Ghulam Fareed Sabri of the Sabri Brothers—had been shot dead in his car in Karachi ten days earlier by the Pakistani Taliban. He’d been praising the Prophet Muhammad (pbuh) and his noble family a little too much for the Taliban’s liking. And so they had their way with him. In a nation inured to violence, Sabri’s death, nevertheless, struck at the communal soul of Pakistan. In the aftermath of the tragedy, the messy confusion of Pakistan’s conflicted national and cultural identity, inflected with the scourge of Wahabism—a tyrannical interpretation of orthodox Islam imported from Saudi Arabia—temporarily dissipated.

Thousands of Pakistanis came out on the streets, united in grief, to protest Sabri’s death. Sabri was a child of Pakistan’s own soil. He belonged to a venerable, centuries-old musical dynasty. His spiritual attunement and the muscular faculty of his voice transported people to ecstasy, raising mere mortals above the denseness of an earthly, mired existence, above differences of class and wealth into a celebration of the Divine. Sabri’s music was a glorification. And it belonged to a distinct tradition of South Asian music, a legacy irrefutably inherent in the DNA of Pakistan, twinned to the devotional practice of Islam and its syncretic cultural roots in the region. Invoking a transcendent joy, Sabri’s qawwali created a milieu of harmony—completely antithetical to the Taliban’s backward, beclouded ideology of hate which thrives on sowing seeds of discord.

On June 28, six days after Sabri’s murder, a triple suicide bombing at Istanbul’s Ataturk International Airport, killed 42 and plunged Turkey—and the world—into shock and mourning. I arrived in Istanbul four days later, and in my mind the two tragedies, Sabri’s death and this latest devastation in Istanbul—and what they both symbolized—became intertwined into a single loss: that of a particular vibrational note, indeed, that of musical harmony. It seemed we were witnessing the slow disintegration of the last bastion of a modernist, secular state in the Islamic world. Of all cities, Istanbul, to me, is the most plausible custodian and embodiment of the kind of “perfect music” of which the Indian musician and mystic Hazrat Inayat Khan, whose teachings bridge East and West, spoke of so cogently.

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by Matt McKenna

Long before the new Ghostbusters film was released, a vocal group of internet commenters had already decided what the movie meant to culture at large. Some commenters thought that the main characters being women was an obvious indicator of an overly politically correct culture. Others thought that the existence of bitter comments about the main characters being women was an appalling indicator of a sexist culture. Battle lines were therefore drawn before the film hit theaters, and the content of the movie appears to be nearly as irrelevant to politically engaged adults as it is to the children who enjoy the Mattel-produced Ghostbusters-branded toy tie-ins. The ultimate combination of politically engaged people and consumerist children, however, met at the Republican National Convention last week. As with Ghostbusters, for politically engaged individuals, the content of the convention was entirely beside the point and merely provided an opportunity to consolidate their faction’s previously held beliefs.

The 2016 Ghostbusters stars Kristen Wiig, Leslie Jones, Kate McKinnon, and Melissa McCarthy replacing Bill Murray, Dan Aykroyd, Harold Ramis, and Ernie Hudson from the original 1984 film of the same name. As with the original, 2016’s Ghostbusters begins with a hapless character (this time played by Zach Woods) being surprised by a ghost. This first scene provides laughs and scares, but the film has trouble maintaining its positive momentum. Though the leads pepper the screen with mostly good jokes, their affability is drowned out by the gooey, disjointed action sequences in which the Ghostbusters crack wise while shooting apparitions.

But I've already wasted too many words on the content of the film–instead I should have written about how my seeing the film served to confirm something I already believe. After all, this is how politics in the United States works: events aren’t input into an opinion-making process, but rather they are shrewdly interpreted to justify a previously held opinion. The Democrat and Republican nominating conventions are prime examples of this sort of confirmation bias. The conventions are unadulterated pomp in which the only output is to remove the “presumptive” qualifier from the “presumptive nominee” title of the candidate who won the primary election. Therefore, the conventions aren’t introspective events where people think about candidates and concerns, but instead they’re places where dissent is squashed and re-branded as “unity.”

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by Bill Benzon and Mary Liebman

On April 27, 2016, Donald Trump opened a foreign policy speech by declaring that he would “develop a new foreign policy direction for our country – one that replaces randomness with purpose, ideology with strategy, and chaos with peace.” He closed by assuring, “American will continually play the role of peacemaker.” If he is serious, then if elected he should create a Peace Office in the White House, an office specifically charged with developing peaceful solutions to foreign policy problems.

For that matter, why doesn't Hillary Clinton hold Trump's feet to the fire and make a peace office a prominent part of the Democratic Platform? Why doesn't Barack Obama beat them to the punch and earn his Nobel Peace Prize by creating such a White House office while he's got the power to do so? Now's the time!

As you may know, the idea was first proposed by Benjamin Rush, one of the founding fathers, in 1793. You may not know that legislation proposing a Department of Peace was before Congress through much of the previous century. That history has been told by Frederick L. Schuman in Why a Department of Peace?, originally published by Another Mother for Peace in 1969. Mother’s efforts were complemented and amplified by the Peace Act Advisory Council (PAAC, which then became Council for a Department of Peace, CODEP). Sitting at her kitchen table with a manual typerwriter and smoking countless cigarettes, Mary Liebman wrote PAX, the group’s newsletter, between 1970 and 1976.

Working with Charlie Keil and with Becky Liebman, Mary’s daughter, I have compiled these and other documents into a pamphlet, We Need a Department of Peace: Everybody’s Business, Nobody’s Job. In the rest of this post I present section six, “Peace is Everybody’s Business, Nobody’s Job”(Mary’s mantra), from the pamphlet. All of the quoted passages are from the newsletters that Mary Liebman wrote.

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by Paul Braterman

Islam Evolving, Taner Edis, Prometheus Books, June 2016

This is an excellent review of an important but difficult subject, and a welcome change from the ill-informed bluster of a Sam Harris, or the limp apologetics of a Karen Armstrong. It is the work of an author who is exceptionally well placed to appreciate the context of the mass of information on which he draws. Lucidly written, it is also a work of broad scholarship (there are more than 500 references and footnotes), and provides an overview of one of the most important developments of our times. Overall, it is a much-needed corrective to the popular view that these times are particularly violent, and that the roots of this violence lie within Islam.

It is also a very disturbing book, and I mean that as a compliment. While fully committed to secular Enlightenment values, Edis recognises that this cannot be the starting position in any worthwhile discussion of committed Islam. Secularism is neither historically inevitable, nor a logical necessity, nor a moral imperative. In his native Turkey, for example, secularism was the founding principle of the modern State, but has lost out to an Islamic pious modernity, whose advocates cannot simply be dismissed as deluded or wicked. Secularism cannot claim to be the more democratic option, where it is not what people would prefer. The secular ideal of rule of an impartial law is not neutral, since it places judges, members of the power elite, as arbiters. Moreover, Edis turns a critical searchlight on the ostensively secular United States, where he now lives and works, finds echoes there of much of what concerns him about Islam today, and challenges the West's air of injured innocence in the face of violence. Ultimately, he regards Islam as a far smaller peril than a rampant neoliberalism that values individuals only as producers and consumers, sells political influence to the highest bidder, and still sponsors the denial of the world's most urgent problem, global warming. He shows how the rhetoric of the “war on terror” is used, in the West as in his native Turkey, to suppress dissent, and is contemptuous of how western defenders of freedom have accepted the facile and counterfactual narrative of an inherently violent Islam. Most disturbing of all, he critically examines his own Enlightenment assumptions, which his readers, and mine, will generally take for granted. For instance, why do we regard free speech as good? To what extent do our own institutions follow this ideal in practice? And should we not be more aware of the degree of coercion implicit in our own social order?

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by Jonathan Kujawa

While I was in graduate school the film “Trekkies” was released. You can see the trailer here and the full film here. What could easily be mocking is in fact a heartfelt look at a group of people who choose to devote their lives to something they love. After seeing the film my friends and I semi-seriously suggested that mathematicians would make a great subject for a documentary. We have more than our share of interesting folks. And, like Trekkies, there is an entire subculture.

One corner of that subculture is Mathematical Reviews. An arm of the American Mathematical Association, Math Reviews is a compendium of everything published in mathematics. It was founded in 1940 and contains over three million publications, with the earliest published in 1810. What makes Math Reviews invaluable is the reviews. Each research paper, monograph, book, etc., is assigned to a volunteer mathematician who has the expertise to write a review of the work. Short of personal attacks, slander, and the like, the reviewer is pretty much free to write what they choose. The usual thing is to give a summary of the work along with commentary. As a reviewer you might discuss how the results fit in the broader field or highlight aspects of the work which might be of particular interest. Oftentimes it's hard to tell from the title and abstract if a paper, say, contains needed results. Well written reviews can save the reader countless hours in the library.

Since reviewers have a free hand there are plenty of exceptional reviews amongst Math Reviews's vast collection. Ten years ago my colleague, Kimball Martin, began a compilation of truly great reviews. If you have access to a library with a subscription to Math Reviews, you can read his entire collection for yourself. Some are rave reviews, but there are some real zingers in there as well (see the title of this essay) which I thought the readers of 3QD would appreciate [1].

With decades worth of publications, some truly terrible papers have appeared. Reviewers aren't ones to let rubbish slide through. Sometimes it is the mathematics itself which is questionable:

It is hard to imagine in a single paper such an accumulation of garbled English, unfinished sentences, undefined notions and notations, and mathematical nonsense. The author has apparently read a large number of books and papers on the subject, if one looks at his bibliography; but it is doubtful that he has understood any of them…. What is amazing to the reviewer is that such a thing was ever printed.

Or:

Not every text containing mathematical formulae or terminology may be considered as a scientific work. Sometimes it is a mere imitation. My impression is that this is exactly the case of the paper under review. The paper deals with some relations between Riemann theta functions, but I have a feeling that the authors have only a rather vague notion about this subject. I doubt that they have read items 1,2,3,6 of their own references. All of the authors' statements are either tautological or false.

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“The Holy Land is everywhere” —Black Elk

Holy Land

moving to one side
out of traffic, off the shoulder
into the weeds, listening

it occures to me that nothing
is tangential, life happens here
regardless

not unscathed
by the mechanical operations of man,
just essentially unmoved

not unscathed
by the myopic visions of man,
but essentially unaware

not unscathed
by the moneyed obsessions of man,
but essentially disinterested

yet all essential to the planet of man
by just belonging to this moment
like secret cogs and wheels:
the unsung, unseen necessities of
breath and beauty
not at all unscathed by the wanton
recklessness of man
.

Jim Culleny
7/14/16

by Misha Lepetic

“The scent, the scent alone is enough for our beasts.”
~ Marinetti

There's that old saying that goes “When the going gets weird, the weird turn pro”. Certainly, weird times such as these demand weird explanations. Old explanatory frameworks that have been dying long, slow deaths continue to have nails pounded into their coffins. Consider how the post-Cold War triumph of neoliberalism, as promoted by Francis Fukuyama's The End Of History, has had the crap beaten out of it first by 9/11, then by the global financial meltdown, and now by Brexit (the best tweet I saw concerning Brexit was all of three words: “Francis Fukuyama lol”).

And no one, least of all Fukuyama, could have predicted the circus slated to begin in Cleveland, with the most unlikely candidate in recent political history about to receive the nomination of the Republican Party for President. Actually, I should amend that: perhaps Upton Sinclair did, 80 years ago. But Sinclair had the dubious benefit of witnessing firsthand the rise of fascism; few people are alive today who remember how wide the Overton Window actually used to be. We need to get much, much weirder.

But it's not just that things are getting weirder. Even more germane is that things are getting weirder, faster. This is nowhere more evident than in the ways in which technologies are insinuating themselves into the social fabric. As I've argued before, each technological development creates the substrate upon which a further, faster and even more unpredictable set of technologies and their circumstances manifests. Perhaps I'm biased, since I've been observing these phenomena for a while, but consider a few recent developments.

Exhibit A: Racially inflected police brutality is an old story. But awareness of it has skyrocketed in the past few years with the prevalence of video cameras. However, this prevalence was only made possible when video recording was bundled into the larger rubric of the smart phone. If video cameras as objects were sufficient unto themselves, we would have seen a very different trajectory following the 1991 Holliday videotape of the Rodney King beating. But it took nearly a full generation for the creation of not only the means of cheap and easy recording, but also its equally cheap and easy distribution. And until recently, even this latter infrastructure was fairly staid: YouTube and perhaps a few other platforms.

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by Brooks Riley (who is standing on the bow of the ship above on September 11, 1959)

The freight trains at night are so loud that in my dreams they become horizontal twin towers spewing sound into the air in horrifying percussive bursts. Sometimes they sound like jumbo jets landing beside my pillow. Or a full-throttle matriarch with her brood in tow. Or Wotan at the height of his wrath in Die Walküre. I know these trains now, their varied speeds and decibels depending on the number of cars trailing the locomotive. If I’m awake I count freight cars instead of sheep, adding up the metronomic ticks of the wheels as they cross a switch.

When I was growing up on the right side of the tracks, I never imagined I would one day live right beside them on another continent. But I do remember a crossing near Berryville, Virginia where the Baltimore & Ohio, (or was it the Chesapeake & Ohio?) snailed by on its way to the rest of the vast country out there. It took 15 minutes and more than 100 freight cars to pass before the barrier was raised (I counted them then, too).

That may be why this little girl wanted a toy train for Christmas. I got one, nothing fancy, just a circular track, a locomotive and a couple of freight cars. I loved its simplicity, the kinetic pleasure of its motorization. Most of my friends were into horses. I was into mechanisms of the vehicular kind, those that could move me from one place to another in an interesting way, or better, take me somewhere. A horse could also fit that bill, but I was rarely allowed to race my pony through the countryside, hair blowing in the wind. I would really do this only years later in Monument Valley when a kindly Navajo let me canter through an arroyo seco without supervision, just like John Wayne in a John Ford Western.

I have a full-scale model train now, right at the front door. It’s nothing to look at, nothing you’d want to open up on Christmas morning, just a deadpan locomotive, a chain of grey tank cars and the occasional thread of flatbeds hauling VW Tiguans in an array of colors to places east of here. I get wanderlust every time I hear it go by.

Those trains have traveled well along the synapses in my brain, their siren songs now identifiable as I play name-that-train with my eyes closed. The Südostbayernbahn is especially witty, with its second locomotive as coda, the extra oomph of base tones filling the air as it mysteriously adds push to pull.

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by Tamuira Reid

I get the call in the middle of night. Calls that come in the middle of the night can never be good. And it isn't.

It's about Amy, the voice on the other end says. It's a voice I don't know. Someone who calls himself her friend, a friend of the family. I wonder where this guy was when Amy was at her worst. I don't remember anyone but me ever sticking around.

The bottom line is she's dead. Gone. Not ever coming back.

Our strip of photo booth pictures are still tucked into my mirror. Happy faces, the newly sober glow. Back when there was still a chance of something good happening.

A year before those photos were taken, Amy left her kids to almost fry to death in her Subaru while she shot dope in a nearby apartment complex. When the judge offered her treatment instead of jail, she cried. She'd rather be high for the rest of her life than constantly replay the moment the ambulance drove off with her two little girls in the back. Two little girls, locked for two hours in a hot car.

I should have just killed myself on the spot, she told me.

And now she's gone, too.

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by Genese Sodikoff

The rabid opposition of American gun owners to stricter gun regulations in the wake of mass shootings is reminiscent of dog owners' opposition to rabies-control measures amidst rashes of “mad dog” attacks in in the late nineteenth and early twentieth centuries. (Poodles in the 1920s were especially mad, for some reason).

Every disease has its particular cultural expression. Societies have their unique spins on the causes and treatments of disease and the experience of suffering. And as I read old newspapers about rabies, it struck me how efforts to control the virus in the United States stirred a familiar anti-government, Freedom-loving, dog-loving ethos, along with a deep distrust of policy-makers and their reasons. In the anti-dog-vax, anti-dog-tax days, some doubted that “hydrophobia,” the clinical term for human rabies, even existed.

Until the 1950s, canine rabies blighted the American cultural landscape and people's inner lives. In Rabid: A Cultural History of the World's Most Diabolical Virus (2012), Bill Wasik and Monica Murphy explain that the rising popularity of pet-keeping in the West made the threat of rabies “an object of disproportionate panic throughout the nineteenth century.” Their gripping book follows the the virus from Ancient Greece to modern medical labs, where scientists are exploiting the rabies peptide as a means to penetrate the blood-brain barrier.

Transported from Europe to America during colonization, and then frequently spilling over from foxes, wolves, raccoons, skunks and bats into domestic animal populations, rabies brought wildness into American towns and cities. Before Louis Pasteur and Emile Roux developed the human rabies vaccine in 1885, the virus destroyed families. Children frequently died of mad dog attacks, as did beloved pets and farm animals.

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by Jalees Rehman

“These terrorists aren't true Muslims” is a phrase that I have often heard being used by American Muslims when talking about terrorist attacks committed in the name of Islam. Recently, I encountered another version of this comment. Parents at a suburban Islamic Sunday School were encouraged to use this same approach when talking to their children about the recent spate of terrorist attacks. Arguments for denying the Muslim identity of the perpetrators include the moral incompatibility of the atrocities committed by the terrorists with Islamic law, which does not sanction the extrajudicial killing of civilians or suicide, which is frequent element of the attacks. This is an understandable reaction. The views of the perpetrators and their actions seem so abhorrent that it is impossible to reconcile their perception of Islam with those of the vast majority of American Muslims. However, even though one may sympathize with the desire to distance oneself from the terrorists, declaring terrorists to be non-Muslims or not “true” Muslims is the wrong answer.

The first problem with the arbitrary post-hoc excommunication of terrorists is that it is not really grounded in Islamic law. The process of takfir (excommunication Islam) requires very strong evidence and is difficult to uphold in most Islamic legal traditions if the person in question continues to see himself or herself as a Muslim. Someone may commit a grave sin or terrible crime, but these actions alone do not propel the person outside of the faith.

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by Scott F. Aikin and Robert B. Talisse

In last month's column, we introduced a name for what we suppose is a familiar phenomenon. Spitballing is a tactic of deflection, where a speaker repeatedly interjects vague, but self-contained, and overtly provocative statements into a discussion. The aim of the spitballer is to overwhelm his interlocutors and critics by providing them with so many outrageous claims that they are unable to adequately reply to any of them. Spitballing is rampant in public political discussion because, in the forums were such discussion commonly occurs, significant benefits accrue to those who appear to the onlooking audience as having gotten the last word.

Spitballing is closely allied with a companion tactic that is also rampant in contemporary public political discussion. Swamping is a tactic for controlling public discourse. Like the spitballer, the swamper introduces into a discussion multiple pointed, self-contained, and overtly provocative statements. Yet the swamper's aim is not to overload his interlocutors, but to dominate the political conversations conducted by others. The swamper's intention is to say something so overtly bizarre or inflammatory as to force others to discuss what he said. In doing so, the swamper seeks not to deflect criticism, but rather to direct political discussion away from the ideas, proposals, policies, and platform of his political competition. As a consequence, the swamper stays at the center of the conversation, forcing every other topic to the periphery. One important motive for swamping is that, in making oneself the topic of conversation by being overtly either vague or controversial, one crowds out time for critical exchange with others. One swamps the competition.

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by Yohan J. John

Human decision-making routinely confounds our attempts at understanding. Right now, the western world is in a state of bafflement and anxiety brought on by unprecedented collective decisions. From the British public's vote to leave the European Union to Republican voters' selection of Donald Trump as their presidential candidate, the past month or so has been a vivid illustration of the unpredictability of human choice.

There is a temptation, particularly among elites who see themselves as well-educated, to see Brexit and the rise of Trump as a failure of intelligence. According to this perspective, disgruntled working class voters are stupid: willfully ignoring the “facts” offered to them by the experts. (Michael Gove has surely captured the spirit of the era with the statement: “People in this country have had enough of experts”.) There may be some truth in the Stupidity Hypothesis, but a far more interesting thing to think about is how statements come to be seen as relevant facts in the first place. And perhaps even more fundamentally, how exactly do facts influence our decisions?

What I would like to say about decision-making strikes me as both obvious and easy to miss. The process of arriving at a decision necessarily involves ignoring information. However much information is available beforehand, at the time a decision is made, much of it is effectively disregarded. And this is not just true of democratic decisions, for which the opinions of the losing side have little or no direct effect on subsequent events. Whenever a situation involves multiple facets, the process of deciding on a course of action involves a simplification that must abstract away from the initial complexity. From a mathematical perspective, decision-making is the process of collapsing a high-dimensional system into a one-dimensional system.

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