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Why the number 2.9013 will go down in the history of bad science
If you’ve been reading this blog for any amount of time you’ll probably be familiar with the name Sokal from the Sokal affair, the scandal in 1996 in which physicist Alan Sokal intentionally submitted a paper that was a steaming pile of horse manure in a leading journal of cultural studies, designed as a test to see if it would get published (spolier, it did).
At the time, Sokal came under harsh criticism from some quarters for creating a "tempest in a tea cup" and for making "tendentious misrepresentations", according to some he had "insufficiently grasped the philosophy (he) criticized". Well the tables have turned and now Sokal along with Nicholas Brown and Harris Friedman have published a paper that mercilessly destroys a paper on positive psychology that has been cited close to a thousand times on Google Scholar and in countless self help books, somehow with no one in the field realizing the paper was not worth the paper it was written on.
The original paper by Fredrickson & Losada makes the case that the “positivity ratio” - the relationship between an individual's positive and negative emotions reaches a critical tipping point when it reaches the number 2.9013.
But as Sokal et al make painfully clear, the paper is utterly brimming with “fundamental conceptual and mathematical errors" and "the total absence of any justiﬁcation for the applicability of the Lorenz equations to modeling the time evolution of human emotions”. With me until that last bit? Well the original paper stated that the “positivity ratio” followed the following, completely irrelevant complex mathematic pattern:
Sokal et al point out that “the idea that any aspect of human behavior or experience should be universally and reproducibly constant to ﬁve signiﬁcant digits would, if proven, constitute a unique moment in the history of the social sciences”. This before demonstrating the fatal mathematical and logical flaws at every level, before concluding “that Fredrickson and Losada’s (2005) claims concerning the alleged critical values of the positivity ratio are entirely unfounded… One can only marvel at the astonishing coincidence that human emotions should turn out to be governed by exactly the same set of equations that were derived in a celebrated article several decades ago as a deliberately simpliﬁed model of convection in ﬂuids, and whose solutions happen to have visually appealing properties”.
The final verdict is damning and enlightening:
“An alternative explanation—and, frankly, the one that appears most plausible to us—is that the entire process of “derivation” of the Lorenz equations has been contrived to demonstrate an imagined ﬁt between some rather limited empirical data and the scientiﬁcally impressive world of nonlinear dynamics.”
The crack team point out the mind bending absurdness of the conclusions Fredrickson and Losada abstract from their unbelievable (in the truest sense of the word) findings:
"They appear to assert that the predictive use of differential equations abstracted from a domain of the natural sciences to describe human interactions can be justiﬁed on the basis of the linguistic similarity between elements of the technical vocabulary of that scientiﬁc domain and the adjectives used metaphorically by a particular observer to describe those human interactions. If true, this would have remarkable implications for the social sciences. One could describe a team’s interactions as “sparky” and conﬁdently predict that their emotions would be subject to the same laws that govern the dielectric breakdown of air under the inﬂuence of an electric ﬁeld. Alternatively, the interactions of a team of researchers whose journal articles are characterized by “smoke and mirrors” could be modeled using the physics of airborne particulate combustion residues, combined in some way with classical optics."
Sokal et al don't postulate with regard to whether the cause of the obviously unlikely finding is the result of "excessive enthusiasm, sincere self-deception, or other motivations".
In a response from Fredrickson (her coauthor has gone mysteriously AWOL), she concedes that “Losada’s mathematical work may have been ﬂawed” - and endeavors to scrub this part of the theory from the record, leaving the original psychological theory intact (which in fairness it may well be, this mumbo jumbo aside).
This all begs the question, how much more of the literature is steeped in fluffy feathered nonsense? “Filigrees of rhetorical precision atop unsteady pillars of conceptual bluff”. The answer is potentially a hefty chunk.
I stumbled on one particularly priceless gem myself only last week, disasters this big are thankfully pretty rare in science, but it just goes to show how important it is to always read critically yourself, even if a thousand other researchers in your field have given something the green light, it doesn’t mean they are right. The whole fiasco reminds me of the bogus TedX talk which received a standing ovation, months went by before it was discovered that the lecture on how “vortel based maths” would save the world was complete and utter unmitigated nonsense.
If anything, my guess would be that this is an example of groupthink, did the researchers that cited this paper really believe it, did they even read it? Or did they see that other esteemed psychologists had cited it and think… “X cited it… must be legit”. It’s something we’re all guilty of doing on some level at some point or another, if we insisted on checking every single “fact” we came across in life ourselves, we’d be both hopelessly ill equipt and have a hard time functioning in society. But when making a scientific argument, or analyzing the particularly earth shattering ones, it’s a practice clearly worth taking up.
Another thing worth pondering is whether this study was so widely cited simply because at first glance it appears more “sciencey” than traditional positive psychology research. In the aftermath of The Seductive Allure of the “Seductive Allure” of Neuroscience Explanations debate, this couldn’t have been more timely.
I’m going to stop here to avoid simply rehashing what has already been said more eloquently elsewhere. For further analysis, I’ll pass you over to the venerable Neuroskeptic over at Discover and Will Willkinson over at the Daily Beast.
Image Credit: Shutterstock/Wikimedia Commons
Update: This article was amended on 23/08/13 to include the line "At the time, Sokal came under harsh criticism from some quarters for creating a "tempest in a tea cup" and for making "tendentious misrepresentations", according to some he had "insufficiently grasped the philosophy (he) criticized" - so that the following remark makes sense in context.
What is human dignity? Here's a primer, told through 200 years of great essays, lectures, and novels.
- Human dignity means that each of our lives have an unimpeachable value simply because we are human, and therefore we are deserving of a baseline level of respect.
- That baseline requires more than the absence of violence, discrimination, and authoritarianism. It means giving individuals the freedom to pursue their own happiness and purpose.
- We look at incredible writings from the last 200 years that illustrate the push for human dignity in regards to slavery, equality, communism, free speech and education.
The inherent worth of all human beings<p>Human dignity is the inherent worth of each individual human being. Recognizing human dignity means respecting human beings' special value—value that sets us apart from other animals; value that is intrinsic and cannot be lost.</p> <p>Liberalism—the broad political philosophy that organizes society around liberty, justice, and equality—is rooted in the idea of human dignity. Liberalism assumes each of our lives, plans, and preferences have some unimpeachable value, not because of any objective evaluation or contribution to a greater good, but simply because they belong to a human being. We are human, and therefore deserving of a baseline level of respect. </p> <p>Because so many of us take human dignity for granted—just a fact of our humanness—it's usually only when someone's dignity is ignored or violated that we feel compelled to talk about it. </p> <p>But human dignity means more than the absence of violence, discrimination, and authoritarianism. It means giving individuals the freedom to pursue their own happiness and purpose—a freedom that can be hampered by restrictive social institutions or the tyranny of the majority. The liberal ideal of the good society is not just peaceful but also pluralistic: It is a society in which we respect others' right to think and live differently than we do.</p>
From the 19th century to today<p>With <a href="https://books.google.com/ngrams/graph?year_start=1800&year_end=2019&content=human+dignity&corpus=26&smoothing=3&direct_url=t1%3B%2Chuman%20dignity%3B%2Cc0" target="_blank" rel="noopener noreferrer">Google Books Ngram Viewer</a>, we can chart mentions of human dignity from 1800-2019.</p><img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDg0ODU0My9vcmlnaW4ucG5nIiwiZXhwaXJlc19hdCI6MTY1MTUwMzE4MX0.bu0D_0uQuyNLyJjfRESNhu7twkJ5nxu8pQtfa1w3hZs/img.png?width=980" id="7ef38" class="rm-shortcode" data-rm-shortcode-id="9974c7bef3812fcb36858f325889e3c6" data-rm-shortcode-name="rebelmouse-image" />
American novelist, writer, playwright, poet, essayist and civil rights activist James Baldwin at his home in Saint-Paul-de-Vence, southern France, on November 6, 1979.
Credit: Ralph Gatti/AFP via Getty Images
The future of dignity<p>Around the world, people are still working toward the full and equal recognition of human dignity. Every year, new speeches and writings help us understand what dignity is—not only what it looks like when dignity is violated but also what it looks like when dignity is honored. In his posthumous essay, Congressman Lewis wrote, "When historians pick up their pens to write the story of the 21st century, let them say that it was your generation who laid down the heavy burdens of hate at last and that peace finally triumphed over violence, aggression and war."</p> <p>The more we talk about human dignity, the better we understand it. And the sooner we can make progress toward a shared vision of peace, freedom, and mutual respect for all. </p>
With just a few strategical tweaks, the Nazis could have won one of World War II's most decisive battles.
- The Battle of Britain is widely recognized as one of the most significant battles that occurred during World War II. It marked the first major victory of the Allied forces and shifted the tide of the war.
- Historians, however, have long debated the deciding factor in the British victory and German defeat.
- A new mathematical model took into account numerous alternative tactics that the German's could have made and found that just two tweaks stood between them and victory over Britain.
Two strategic blunders<p>Now, historians and mathematicians from York St. John University have collaborated to produce <a href="http://www-users.york.ac.uk/~nm15/bootstrapBoB%20AAMS.docx" target="_blank">a statistical model (docx download)</a> capable of calculating what the likely outcomes of the Battle of Britain would have been had the circumstances been different. </p><p>Would the German war effort have fared better had they not bombed Britain at all? What if Hitler had begun his bombing campaign earlier, even by just a few weeks? What if they had focused their targets on RAF airfields for the entire course of the battle? Using a statistical technique called weighted bootstrapping, the researchers studied these and other alternatives.</p><p>"The weighted bootstrap technique allowed us to model alternative campaigns in which the Luftwaffe prolongs or contracts the different phases of the battle and varies its targets," said co-author Dr. Jaime Wood in a <a href="https://www.york.ac.uk/news-and-events/news/2020/research/mathematicians-battle-britain-what-if-scenarios/" target="_blank">statement</a>. Based on the different strategic decisions that the German forces could have made, the researchers' model enabled them to predict the likelihood that the events of a given day of fighting would or would not occur.</p><p>"The Luftwaffe would only have been able to make the necessary bases in France available to launch an air attack on Britain in June at the earliest, so our alternative campaign brings forward the air campaign by three weeks," continued Wood. "We tested the impact of this and the other counterfactuals by varying the probabilities with which we choose individual days."</p><p>Ultimately, two strategic tweaks shifted the odds significantly towards the Germans' favor. Had the German forces started their campaign earlier in the year and had they consistently targeted RAF airfields, an Allied victory would have been extremely unlikely.</p><p>Say the odds of a British victory in the real-world Battle of Britain stood at 50-50 (there's no real way of knowing what the actual odds are, so we'll just have to select an arbitrary figure). If this were the case, changing the start date of the campaign and focusing only on airfields would have reduced British chances at victory to just 10 percent. Even if a British victory stood at 98 percent, these changes would have cut them down to just 34 percent.</p>
A tool for understanding history<p>This technique, said co-author Niall Mackay, "demonstrates just how finely-balanced the outcomes of some of the biggest moments of history were. Even when we use the actual days' events of the battle, make a small change of timing or emphasis to the arrangement of those days and things might have turned out very differently."</p><p>The researchers also claimed that their technique could be applied to other uncertain historical events. "Weighted bootstrapping can provide a natural and intuitive tool for historians to investigate unrealized possibilities, informing historical controversies and debates," said Mackay.</p><p>Using this technique, researchers can evaluate other what-ifs and gain insight into how differently influential events could have turned out if only the slightest things had changed. For now, at least, we can all be thankful that Hitler underestimated Britain's grit.</p>
A new study shows our planet is much closer to the supermassive black hole at the galaxy's center than previously estimated.
Arrows on this map show position and velocity data for the 224 objects utilized to model the Milky Way Galaxy. The solid black lines point to the positions of the spiral arms of the Galaxy. Colors reflect groups of objects that are part of the same arm, while the background is a simulation image.
Apple sold its first iPod in 2001, and six years later it introduced the iPhone, which ushered in a new era of personal technology.