Posts Tagged ‘knowledge’
“Life is a Zen koan, that is, an unsolvable riddle. But the contemplation of that riddle – even though it cannot be solved – is, in itself, transformative.”*…
How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. And as Ben Brubaker explains, a string of recent results has started to deliver answers…
… Even seasoned researchers find understanding in short supply when they confront the central open question in theoretical computer science, known as the P versus NP problem. In essence, that question asks whether many computational problems long considered extremely difficult can actually be solved easily (via a secret shortcut we haven’t discovered yet), or whether, as most researchers suspect, they truly are hard. At stake is nothing less than the nature of what’s knowable.
Despite decades of effort by researchers in the field of computational complexity theory — the study of such questions about the intrinsic difficulty of different problems — a resolution to the P versus NP question has remained elusive. And it’s not even clear where a would-be proof should start.
“There’s no road map,” said Michael Sipser, a veteran complexity theorist at the Massachusetts Institute of Technology who spent years grappling with the problem in the 1980s. “It’s like you’re going into the wilderness.”
It seems that proving that computational problems are hard to solve is itself a hard task. But why is it so hard? And just how hard is it? Carmosino and other researchers in the subfield of meta-complexity reformulate questions like this as computational problems, propelling the field forward by turning the lens of complexity theory back on itself.
“You might think, ‘OK, that’s kind of cool. Maybe the complexity theorists have gone crazy,’” said Rahul Ilango, a graduate student at MIT who has produced some of the most exciting recent results in the field.
By studying these inward-looking questions, researchers have learned that the hardness of proving computational hardness is intimately tied to fundamental questions that may at first seem unrelated. How hard is it to spot hidden patterns in apparently random data? And if truly hard problems do exist, how often are they hard?
“It’s become clear that meta-complexity is close to the heart of things,” said Scott Aaronson, a complexity theorist at the University of Texas, Austin.
This is the story of the long and winding trail that led researchers from the P versus NP problem to meta-complexity. It hasn’t been an easy journey — the path is littered with false turns and roadblocks, and it loops back on itself again and again. Yet for meta-complexity researchers, that journey into an uncharted landscape is its own reward. Start asking seemingly simple questions, said Valentine Kabanets, a complexity theorist at Simon Fraser University in Canada, and “you have no idea where you’re going to go.”…
Complexity theorists are confronting their most puzzling problem yet– complexity theory itself: “Complexity Theory’s 50-Year Journey to the Limits of Knowledge,” from @benbenbrubaker in @QuantaMagazine.
* Tom Robbins
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As we limn limits, we might send thoroughly cooked birthday greetings to Denis Papin; he was born on this date in 1647. A mathematician and physicist who worked with Christiaan Huygens and Gottfried Leibniz, Papin is better remembered as the inventor of the steam digester, the forerunner of the pressure cooker and of the steam engine.
“The mainstream narrative that we are living through an era of exponential, near-infinite knowledge accumulation no longer fits a society in which we lose our collective record of ourselves day in and day out”*…
Political and government bans and censorship, publishers attacking digital access/ lending— there’s a growing struggle underway (in the U.S. and abroad) that will define how humanity’s collective digital memory is owned, shared, and preserved — or lost forever. Nanna Bonde Thylstrup on why we must care…
… The fact that crucial decisions about whether to keep or destroy data are kept in the hands of actors with profit motives, autocratic aspirations or other self-serving ends has a huge implication not only for individuals but also for the culture at large.
Many instances of data loss have ramifications for cultural production, the writing of history and, ultimately, the practice of democracy…
Alongside the need to maintain public trust in democratic institutions, we must consider how we ought to preserve our collective cultural memory. Institutions like museums, libraries and archives must play a more proactive role while creating stronger institutional safeguards — including rules mandating secure transport of public sector data and professional management of archives, in addition to requirements for public accessibility — on their own conduct. These organizations, whether they are upstart archival initiatives or established public institutions, require stable financial and institutional support to flourish…
The history of knowledge is not one of simple progress or accumulation. Knowledge production in the digital era, like the creation and storage of knowledge across the centuries, is unfolding as a continual oscillation between gains and losses.
Data loss on a small scale — missing phone contacts, digital files lost to a glitch — is the occupational hazard of existing in a digitally reliant world. But data erasure at scale is always political. Responses to erasure and loss must exceed technical fixes and knee-jerk reactions; instead, governments and organizations must constantly reassess the ethical and regulatory frameworks that govern our relationship with data. The mainstream narrative that we are living through an era of exponential, near-infinite knowledge accumulation no longer fits a society in which we lose our collective record of ourselves day in and day out…
Eminently worth reading in full: “The World’s Digital Memory Is at Risk” (gift link)
Pair with the Internet Archive‘s Brewster Kahle‘s “Our Digital History Is at Risk” and Richard Ovenden‘s important (and engrossing) Burning the Books.
* Nanna Bonde Thylstrup
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As we prioritize preservation and open access, we might recall that it was on this date in 1978 that the Rainbow Flag was flown for the first time during the San Francisco Gay Freedom Day Parade. Created by Gilbert Baker, it has become a sign of LGBTQ pride worldwide.
“There is only one good, knowledge, and one evil, ignorance”*…
If only it were that simple. Trevor Klee unpacks the travails of Galileo to illustrate the way that abstractions become practical “knowledge”…
… We’re all generally looking for the newest study, or the most up-to-date review. At the very least, we certainly aren’t looking through ancient texts for scientific truths.
This might seem obvious to you. Of course you’d never look at an old paper. That old paper was probably done with worse instruments and worse methods. Just because something’s old or was written by someone whose name you recognize doesn’t mean that it’s truthful.
But why is it obvious to you? Because you live in a world that philosophy built. The standards for truth that you imbibed as a child are not natural standards of truth. If you had been an educated person in 1200s Europe, your standard for truth would have been what has stood the test of time. You would have lived among the ruins of Rome and studied the anatomy texts of the Greek, known that your society could produce neither of those, and concluded that they knew something that your society could not. Your best hope would then be to simply copy them as best as possible.
This was less true by the time Galileo was alive. This is why an educated man like Galileo would have entertained the idea that he knew better than the ancient Greeks, and why his ideas found some purchase among his fellow academicians (including the then Pope, actually). But still, there was a prominent train of thought that promoted the idea that a citation from Aristotle was worth more than a direct observation from a telescope.
But you live in a different world now. You live in a world in which the science of tomorrow is better than the science of today, and our societal capabilities advance every year. We can build everything the ancients did and stuff they never even imagined possible. So you respect tradition less, and respect what is actually measured most accurately in the physical world more.
Today, this battle over truth is so far in the past that we don’t even know it was ever a battle. The closest we come to this line of reasoning is when new age medicine appeals to “ancient wisdom”, but even they feel compelled to quote studies. Even more modern battles are mostly settled, like the importance of randomized, double-blinded controlled studies over non-randomized, non-controlled studies.
The reason we mark battles is not just for fun or historical curiosity. It’s to remind us that what we take for granted was actually fought for by generations before us. And, it’s to make sure that we know the importance of teaching these lessons so thoroughly that future generations take them for granted as well. A world in which nobody would dream of established theory overturning actual empirical evidence is a better world than the one that Galileo lived in…
On the importance of understanding the roots of our understanding: “You live in a world that philosophy built,” from @trevor_klee via @ByrneHobart.
Apposite (in an amusing way): “Going Against The Grain Weevils,” on Aristotle’s Generation of Animals and household pests.
* Socrates, from Diogenes Laertius, Lives and Opinions of Eminent Philosophers (probably early third century BCE)
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As we examine epistemology, we might send elegantly phrased and eclectic birthday greetings to Persian polymath Omar Khayyam; the philosopher, mathematician, astronomer, epigrammatist, and poet was born on this date in 1048. While he’s probably best known to English-speakers as a poet, via Edward FitzGerald’s famous translation of (what he called) the Rubaiyat of Omar Khayyam, Fitzgerald’s attribution of the book’s poetry to Omar (as opposed to the aphorisms and other quotes in the volume) is now questionable to many scholars (who believe those verses to be by several different Persian authors).
In any case, Omar was unquestionably one of the major philosophers, mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. His astronomical observations contributed to the reform of the Persian calendar. And he made important contributions to mechanics, geography, mineralogy, music, climatology and Islamic theology.
“For the sake of the science, it might be time for scientists to start trusting each other a little less”*…
We’ve looked at methodical problems in scientific and medical research before (see here, here, and here). Let us turn now to outright dishonesty. The rising number of retracted research papers suggests that either medical research fraud is on the rise or that efforts to spot it are getting better. Either way, it’s a problem …
… Partly or entirely fabricated papers are being found in ever-larger numbers, thanks to sleuths like Dr Mol. Retraction Watch, an online database, lists nearly 19,000 papers on biomedical-science topics that have been retracted (see chart 1). In 2022 there were about 2,600 retractions in this area—more than twice the number in 2018. Some were the results of honest mistakes, but misconduct of one sort or another is involved in the vast majority of them…
… Yet journals can take years to retract, if they ever do so. Going by these numbers, roughly one in 1,000 papers gets retracted. That does not sound too bad. However, Ivan Oransky, one of Retraction Watch’s founders, reckons, based on various studies of the matter and reports from sleuths, that something more like one in 50 papers has results which are unreliable because of fabrication, plagiarism or serious errors…
… It is often asserted that science is self-correcting. And it is true that, if a claimed result is important enough, an inability to replicate it or of subsequent work to conform to it will eventually be noticed. In the short term, though, it is easy to hide in the shadows. Even co-authors of a data-fabricating scientist—those, in other words, who are closest to him or her—may not notice what the culprit is up to. In complex studies of a particular disease, several types of researchers will be involved, who are, by definition, not experts in each other’s fields. As Dr Bishop observes, “You just tend to take on trust the bits of data that somebody else has given you.”…
In the end, however, keeping fakes out of the scientific record depends on the willingness of publishers to stump up more resources. Statistical checks of clinical-trial papers often involve laborious manual work, such as typing up specific data in spreadsheets. This would require journals to hire dedicated staff, cutting into profits.
Many academics who have spent years trying to get fabricated papers retracted are pessimistic that better ways to detect fraud will, alone, make a big difference. Dr Roberts and Dr Mol want journals to be regulated in the way that social media and the news business are in some countries, with standards on what they publish. Peter Wilmshurst, a British cardiologist who has raised the alarm about numerous cases of research misconduct in his field, thinks there should be criminal penalties for those who fabricate data. Dr Gunsalus wants universities to make public the reports from their research-fraud investigations. And everyone agrees that publish or perish is a recipe for disaster.
None of these solutions will be quick or straightforward. But it is now clear that choosing to look the other way is causing palpable harm to patients…
“There is a worrying amount of fraud in medical research- and a worrying unwillingness to do anything about it,” from @TheEconomist.
* Stuart Ritchie, Science Fictions
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As we look harder, we might spare a thought for Alfred Habdank Skarbek Korzybski; he died on this date in 1950. Trained as an engineer, he developed a field called general semantics, which he viewed as both distinct from, and more encompassing than, the field of semantics. He argued that human knowledge of the world is limited both by the human nervous system and the languages humans have developed, and thus no one can have direct access to reality, given that the most we can know is that which is filtered through the brain’s responses to reality. (Korzybski assumed that the quest for knowledge was an authentic, honest one; that said, if “human nervous system” an be understood to extend to “human nature”…)
Korzybski was influential in fields across the sciences and humanities through the 1940s and 50s (perhaps most notably, gestalt therapists), and inspired science fiction writers (like Robery Heinlein and A.E. van Vogt) and philosophers like Alan Watts.
His best known dictum is “The map is not the territory.”
“I would rather have questions that can’t be answered than answers that can’t be questioned”*…
… or, as Confucius would have it, “real knowledge is to know the extent of one’s ignorance.” Happily Wikenigma is here to help…
Wikenigma is a unique wiki-based resource specifically dedicated to documenting fundamental gaps in human knowledge.
Listing scientific and academic questions to which no-one, anywhere, has yet been able to provide a definitive answer. [949 so far]
That’s to say, a compendium of so-called ‘Known Unknowns’…
Consider, for example…
How do marine turtle accurately migrate thousands of kilometers for nesting?
Can Beal’s conjecture be proved?
Can one solve the “envelope paradox”?
Do “naked singularities” exist?
What is the etymology of the word “plot” (which appears only in English)?
What are the function, importance, and evolutionary history of human “inner speech”?
One could– and should– go on: Wikenigma, via @Recomendo6.
* Richard Feynman
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As we wonder, we might spare a thought for a man who embodied curiosity, Marvin Minsky; he died on this date in 2016. A biochemist and cognitive scientist by training, he was founding director of MIT’s Artificial Intelligence Project (the MIT AI Lab). Minsky authored several widely-used texts, and made many contributions to AI, cognitive psychology, mathematics, computational linguistics, robotics, and optics. He holds several patents, including those for the first neural-network simulator (SNARC, 1951), the first head-mounted graphical display, the first confocal scanning microscope, and the LOGO “turtle” device (with his friend and frequent collaborator Seymour Papert). His other inventions include mechanical hands and the “Muse” synthesizer.
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