You’re then told that’s a no-no and that’s because zeros and infinities lead to all kinds of arithmetic “bad behavior” or singularities.
You’re then supposed to see that x2 – 1 can be re-written as (x – 1)(x + 1) and since “like cancels like,” you cancel the x – 1 is the numerator and denominator and “get rid” of it.
This leaves simply x + 1. So, as x goes to 1, x + 1 goes to 2 and you have a “legitimate” answer and have bypassed the impasse of 0 acting badly (i.e., zero divided by zero).
If you re-understand all this more slowly you’ll see that there are endless potential confusions:
For example: you cannot say that (x2 – 1)/(x – 1) = x + 1 since looking at the two sides of the equal sign shows different expressions which are not equal.
Math and science for that matter, are based on taking a formula or expression (like the one we saw above) and “de-cluttering” it or “shaking loose” a variant form which is not identical and not the same but functionally equivalent in a restricted way.
A lot of students who fail to follow high school or collegescience sense these and other “language and number” problems of hidden vagueness. School courses punish students who “muse” to themselves about hidden vagueness. This behavior is pre-defined as “bad woolgathering” but we turn this upside down and claim it is potentially “good woolgathering” and might lead to enchantment which then underlies progress in getting past one’s fear of something like math or science or anything else.
Think of daily life: you say to someone: “you can count one me.” You mean trust, rely on, depend on, where count on is a “set phrase.” (The origin of the phrase and how it became a set phrase is probably unknowable and lost in the mists of time.)
“You can count on me” does not mean you can stand on me and then count something…one, two, three.
In other words in all kinds of language (English, say, or math as a language) one is constantly “skating over” such logic-and-nuance-and-meaning issues.
The genius Kurt Gödel (Einstein’s walk around buddy at Princeton) saw this in a deep way and said that it’s deeply surprising that languages work at all (spoken, written or mathematical) since the bilateral sharing of these ambiguities would seem deadly to any clarity at all and communication itself would seem a rather unlikely outcome.
The Brain Bank has released findings from its first three years of operation, analyzing the brains of professional and non-professional athletes who donate them after death.
The researchers say 12 of the athletes’ brains showed signs of chronic traumatic encephalopathy (CTE), a condition associated with a range of psychiatric problems, ranging from mood and behavior disorders to cognitive impairment and dementia.
“CTE was identified in the brains of older former professionals with long playing careers, but also in younger, non-professional sportsmen and in recent professionals who had played under modern concussion guidelines,” the authors found.
“Screening for CTE in all deaths by suicide is probably impractical, but our finding suggests it should be undertaken if a history of repetitive head injury is known or suspected,” the authors say.
The authors note that brains donated to the bank are more likely to show signs of trauma because donation is often done when an athlete’s family have concerns about the role head trauma may have played in a person’s death or condition.
Nonetheless, they say: “Our findings should encourage clinicians and policymakers to develop measures that further mitigate the risk of sport-related repetitive head injury.”
One Step Closer to Hydrogen-Fueled Planes
Airbus to Test Zero-Emissions Aircraft, but How Does It Work?
Hydrogen fuel, touted by some as the fuel of the future, is seen as a potential solution for the deeply polluting aviation and shipping industries in a net-zero world: hydrogen burns cleanly, producing just energy and water vapor.
But while engineers have promoted hydrogen as a possible transport fuel since at least the 1920s, real-world technologies are still in their infancy, thanks to the destructive dominance of fossil fuels over the last century.
Airbus’ announcement, then, marks an important early step in a move towards making the sector compatible with net-zero.
“This is the most significant step undertaken at Airbus to usher in a new era of hydrogen-powered flight since the unveiling of our ZEROe concepts back in September 2020,” said Sabine Klauke, Airbus Chief Technical Officer, in a statement.
“By leveraging the expertise of American and Europeanengine manufacturers to make progress on hydrogen combustion technology, this international partnership sends a clear message that our industry is committed to making zero-emission flight a reality.”
“Our ambition is to take this aircraft and add a stub in between the two rear doors at the upper level,” said Glenn Llewellyn, Airbus’ Vice President of Zero Emissions Aircraft, in a promotional video on YouTube. “That stub will have on the end of it a hydrogen powered gas turbine.”
There will be instruments and sensors around the hydrogen storage unit and engine, to monitor how the system functions both in ground tests and in-flight. Up in the cockpit, instruments will need to be modified with a new throttle to change the amount of power the engine operates at, and a display for pilots to monitor the system.
Why Hydrogen Fuel?
Hydrogen, the most abundant element in the Universe, burns cleanly, and can be produced using renewable energy through the electrolysis of water (though it can be produced using fossil fuels, too).
Given that it’s so abundant, can be made from water, and combusts to produce water vapor, it can be a closed-loop energy system; the definition of renewable.
It’s also highly reactive: hydrogen gas, made up of two hydrogen atoms, can combust at extremely low concentrations. It can combust in response to a simple spark, and it’s even been known to combust when exposed to sunlight or minor increases in temperature. That’s why it’s a suitable replacement fuel for kerosene, but it’s also why the system needs to be tested for safety.
“Aviation is one of these things that everyone agrees needs hydrogen for decarbonization, because it’s not going to be possible to electrify long distance air travel in the next few decades,” explains Fiona Beck, a senior lecturer at ANU and convener of the Hydrogen Fuels Project in the University’s Zero-carbon energy for the Asia Pacific grand challenge. “We just don’t have the battery technologies.
“One kilogram of hydrogen has 130 times the energy of one kilogram of batteries, so in something like air travel, where weight is really important, there’s just no way you’re going to get batteries light enough to directly electrify air travel.”
That’s a very high-profile incident in which hydrogen proved deadly, but a proverbial boatload of hydrogen gas encased within a fabric covering is nothing like the fuel cells proponents of hydrogen fuel are creating in the modern era.
Nonetheless, the incident demonstrates why it’s important to ensure the safety and impregnability of fuel storage; a single spark can prove fatal (though that’s the case with existing fuels, too).
“The key will be to have really good storage containers for the hydrogen, and you’re going to have to re-engineer all the fuel delivery lines,” says Beck, “because you can’t assume that the systems that deliver kerosene safely to an engine are going to be suitable for delivering hydrogen.”
Ultimately, Beck says pre-existing, sophisticated hydrogen technologies, even if they aren’t derived from aviation, mean engineers aren’t going into this blind.
“We already use quite a lot of hydrogen in industry, which is very different than flying a plane full of hydrogen, but still, we know how to handle it relatively safely.
“So, it’s just about designers and engineers making sure that they consider all the safety aspects of it. It’s different, but not necessarily more challenging.”
Two Paths to a Hydrogen Fueled Future of Flight?
Beck notes that Airbus aren’t the only commercial entity exploring hydrogen as a fuel type. In fact, Boeing are incorporating hydrogen into their vision of a cleaner future, but in a different way.
“There’s a difference between just getting hydrogen and burning it in a modified jet engine and what Boeing are doing, which is using sustainable air fuels,” she says.
But what are sustainable air fuels (SAFs)? Beck says they’re made by combining hydrogen with carbon dioxide to make a sustainably-produced kerosene.
“The difference is that instead of getting fossil fuels and refining them, you start with hydrogen, which you would hope comes from green sources, and then you take some carbon dioxide captured from another industrial process, and you’re cycling the carbon dioxide one more time before it gets released.”
So, CO2 is still released into the atmosphere, but the individual flight is not adding its own new load of greenhouse gases to the amount. Instead, it essentially piggy-backs off a pre-existing quantity of emissions that were already produced somewhere else.
The type of fuel that wins out remains to be seen.
“It’ll be really interesting to see which approach we go for in the longer term,” Beck muses. “With synthetic air fuels, your plane engine doesn’t need to change at all, nothing about the demand side needs to change–it’s just kerosene.
“But then there’s issues, because you’re still using carbon dioxide.”
Some commentators see Boeing’s bet on SAFs as a more pragmatic approach that may help us usher in a less polluting age, quicker. On the other hand, if successful, the Airbus system can be fully carbon-neutral from fuel production through to combustion.
“Climate Adaptation by Itself Is Not Enough”: The Latest IPCC Report Installment
The Second of Three Reports Shows Our Vulnerabilities and How We Can Protect Them.
In the next part of its Sixth Assessment Report, released today, the IPCC has examined the world population’s vulnerability to climate change, and what must be done to adapt to current and future changes.
It’s the second of three sections of this report (Working group II)–Working Group I’s section, released last August, demonstrates that anthropogenic climate change is continuing, while Working Group III’s component, on mitigation, will be released in April. An overall report is coming in September.
The IPCC reports represent a phenomenal amount of work from hundreds of researchers and government officials. It synthesizes information from over 10,000 studies, with over 62,000 comments from expert peer reviewers.
Literally every sentence of the summary for policymakers has been agreed upon by consensus from a group of experts and government delegations–the line-by-line approval process alone takes a fortnight. The report in its entirety is a product of several years.
Given the time and expertise involved in making the report, its conclusions aren’t revelatory: the world is becoming increasingly vulnerable to the effects of climate change, poorest people are often the most at risk, and adaptation to these effects will force changes in our lifestyle, infrastructure, economy and agriculture.
While adaptation is necessary, it’s also insufficient. “It’s increasingly clear that the pace of adaptation across the globe is not enough to keep up with climate change,” says Professor Mark Howden, Working Group II’s vice-chair and director of the Institute for Climate, Energy & Disaster Solutions at the Australian National University.
Under the IPCC’s projected emissions scenarios, the climate could warm much more or slightly more, based on the volume of greenhouse gas released into the atmosphere.
“Depending on which of those trajectories we go on, our adaptation options differ,” says Howden.
On our current, business-as-usual trajectory, we can’t avoid the crisis, no matter how much we change our human systems to prepare for or recover from the ravages of climate change.
“Climate adaptation, risk management, by itself is not enough,” says Howden.
The report comes at a pertinent time for Australia, as southern Queensland and northern New South Wales experience dramatic flooding from high, La Niña-related rainfall.
“One of the clear projections is an increase in the intensity of heavy rainfall events,” says Professor Brendan Mackey, director of National Climate Change Adaptation Research Facility at Griffith University, and a lead author on the Australasian chapter of the report.
Mackey also notes that he has extended family members in Lismore, NSW, who today needed to be rescued from their rooftops as the town floods.
Howden says that while it’s hard to link individual disasters to climate change as they occur, he agrees that there are more floods projected for northern Australia.
“I think we can say that climate change is already embedded in this event,” adds Howden.
“These events are driven by, particularly, ocean temperatures, and we know very well that those have gone up due to climate change due to human influence.”
He points out that flooding is a common side effect of a La Niña event, of which more are expected as the climate warms.
Flooding is not the only extreme weather event that can be linked to climate change.
“We’ve observed further warming and sea level rise, we’ve observed more flood days and heat waves, we’ve observed less snow,” says Mackey.
“Interestingly, [we’ve observed] more rainfall in the north, less winter rainfall in the southwest and southeast, and more extreme fire weather days in the south and east.”
All of these trends are expected to continue, especially under high-emissions scenarios.
For Australians, the predictions the IPCC has made with very high or high confidence include: both a decline in agricultural production and increase in extreme fire weather across the south of the continent; a nation-wide increase in heat-related mortality; increased stress on cities, infrastructure and supply chains from natural disasters; and inundation of low-lying coastal communities from sea level rise.
The final high-confidence prediction is that Australian institutions and governments aren’t currently able to manage these risks.
“Climate change impacts are becoming more complex and difficult to manage,” says Professor Lauren Rickards, director of the Urban Futures Enabling Capability Platform at RMIT, also a lead author on the Australasian chapter.
“Not only are climatic hazards becoming more severe–including, sometimes, nonlinear effects such as, for example, tipping over flood levees that have historically been sufficient–but also those climatic hazards are intersecting in very, very complex ways. And in turn, the flow-on effects on the ground are interacting, causing what’s called cascading and compounding impacts.”
She adds that many local and state governments and the private sector have both recognized the importance of changing their practices to prepare for or react to climate extremes.
“We have these systems, these infrastructural systems–energy, transport, water, communications, for example–and it’s the need to adapt those at the base of a lot of the adaptation that’s needed,” says Rickards.
Australia is missing a large investment in research on how different places and systems can adapt to the changing climate.
“We’ve seen a really significant reduction in the research into what actions different individuals, communities, sectors, can take,” says Howden.
“And what that means is we don’t have the portfolio of options available for people in a way that is easily communicable, and easily understood, and easily adopted.”
Without this research, as well as work from local and Indigenous experts, some adaptations can even risk worsening the impacts of climate change.
“The evidence that we’ve looked at shows really clearly that adaptation strategies, when they build on Indigenous and local knowledge and integrate science, that’s when they are most successful,” says Dr. Johanna Nalau, leader of the Adaptation Science Research Theme at Cities Research Institute, Griffith University.
While the risks Australia faces are dramatic, things are much worse for other parts of the world. Nalau, who was a lead author on the report’s chapter on small islands, says that “most of the communities and countries are constrained in what they can do in terms of adaptation”.
In April, we will have access to the IPCC’s dossier on mitigating climate change and emissions reduction. But in the meantime, Working Group II’s battalion of researchers advocate for better planning for climate disaster, more research into ways human systems can adapt, sustainable and just development worldwide, and rapid emissions reduction.
“Adaptation can’t be divorced from mitigation, conceptually or in practice,” says Rickards.
“We need adaptation to enable effective mitigation. We need effective mitigation to enable adaptation to give it a chance of succeeding. At present, we’re not on track and we need to pivot quickly.”
Piecing Together Pandemic Origins
New Research Asserts Market, Not Laboratory, Is the “Unambiguous” Birthplace of SARS-CoV-2
by Jamie Priest
Now in our third year of woe, most of us are naturally focused on the end of the pandemic. The global death toll is approaching 6 million, and the world is desperately searching for signs the ordeal’s over.
But amid the future watching, a team of researchers have turned their attention back to the beginning, tackling the question that was once on everyone’s lips: where did SARS-CoV-2 originate?
Outlining their evidence in two preprints, researchers assert an “unambiguous” origin in the Huanan market in Wuhan, spilling over not once, but twice into the human population and kicking off a global health crisis.
The paired papers, which have yet to undergo peer review and publication in a scientific journal, critically undermine the competing, and controversial, alternative origin story that involves a leak–intentional or otherwise–from a nearby Wuhan virology lab where scientists study coronaviruses.
The Huanan market was an immediate suspect when COVID first emerged in late 2019. Workers at the market were amongst the first individuals to present with the pneumonia that was quickly linked to a novel coronavirus, and Chinese officials, fearing a repeat of the 2002 SARS epidemic that killed 774 people, were quick to close the market down.
But by the time Chinese researchers descended on the Huanan market in 2020 to collect genetic samples, they found no wildlife present at all. Although they were able to detect traces of the virus in samples taken from surfaces and sewers in the market, the lack of direct evidence of infection in market animals sparked a debate over whether this truly was the epicenter of the outbreak. Alternative theories centered around the Wuhan Institute of Virology.
In the face of this absence of evidence, researchers working on the new reports turned to alternative information sources.
Using data pulled from the Chinesesocial media app Weibo, they were able to map the location of 737 COVID-positive Wuhan residents who turned to the app to seek health advice during the first three months of the outbreak.
Plotting the geographic concentrations of cases through time, the researchers clearly identified the market as the centre of origin, with the virus spreading radially through surrounding suburbs and across the city as time progressed. Through statistical analysis, the researchers demonstrated that the chances of such a pattern arising through mere chance was exceedingly unlikely.
However, the pattern alone was open to interpretation, with questions remaining about pathways of introduction to the market–was the virus carried in inside a caged animal, on the coat of an unwitting scientist, or via some as-yet unidentified vector?
To dig further into the mystery, the researchers looked at the genetic samples obtained from market surfaces in January 2020 by Chinese scientists, tracing the locations of individual positive samples to their exact location within the market complex.
This second map revealed a strong concentration of positive samples in one corner of the market, a sector that had been previously documented to house a range of wild mammals that are considered potential coronavirus hosts.
Finally, the researchers created an evolutionary family tree of the earliest coronavirus lineages that emerged in the first few panicked weeks of the pandemic.
Even in its very earliest stages SARS-CoV-2 was a variable beast, with evidence of two distinct lineages, dubbed A and B. Looking closely at the mutations that separate the two, the researchers found something surprising–rather than one descending from the other, it appears that they had separate origins and entries into the human population, with lineage B making the leap in late November and lineage A following suit shortly afterwards.
Initial studies of the Huanan market genetic samples found only lineage B, but this latest investigation detected the presence of lineage A in people who lived in close proximity to the market–a finding corroborated by a recent Chinese study that identified lineage A on a single glove collected from the market during the initial shutdown.
Questions remain about the identity of the intermediary animal host species. But by narrowing research focus to the most likely centre of origin, this research will significantly aid efforts to understand the process that saw COVID-19 enter the world, and hopefully help avert future pandemics.
Fake Viral Footage Is Spreading alongside the Real Horror in Ukraine—Here Are 5 Ways to Spot It
Manipulated or Falsified Videos and Images Can Spread Quickly—but There Are Strategies You Can Take to Evaluate Them.
By TJ Thompson, Daniel Angus and Paul Dootson
Amid the alarming images of Russia’s invasion of Ukraine over the past few days, millions of people have also seen misleading, manipulated or false information about the conflict on social media platforms such as Facebook, Twitter, TikTok and Telegram.
One example is this video of military jets posted to TikTok, which is historical footage but captioned as live video of the situation in Ukraine.
Visuals, because of their persuasive potential and attention-grabbing nature, are an especially potent choice for those seeking to mislead. Where creating, editing or sharing inauthentic visual content isn’t satire or art, it is usually politically or economically motivated.
Disinformation campaigns aim to distract, confuse, manipulate and sow division, discord, and uncertainty in the community. This is a common strategy for highly polarized nations where socioeconomic inequalities, disenfranchisement and propaganda are prevalent.
How is this fake content created and spread, what’s being done to debunk it, and how can you ensure you don’t fall for it yourself?
What Are the Most Common Fakery Techniques?
Using an existing photo or video and claiming it came from a different time or place is one of the most common forms of misinformation in this context. This requires no special software or technical skills—just a willingness to upload an old video of a missile attack or other arresting image, and describe it as new footage.
Another low-tech option is to stage or pose actions or events and present them as reality. This was the case with destroyed vehicles that Russia claimed were bombed by Ukraine.
Using a particular lens or vantage point can also change how the scene looks and can be used to deceive. A tight shot of people, for example, can make it hard to gauge how many were in a crowd, compared with an aerial shot.
Taking things further still, Photoshop or equivalent software can be used to add or remove people or objects from a scene, or to crop elements out from a photograph. An example of object addition is the below photograph, which purports to show construction machinery outside a kindergarten in eastern Ukraine. The satirical text accompanying the image jokes about the “calibre of the construction machinery”—the author suggesting that reports of damage to buildings from military ordinance are exaggerated or untrue.
Close inspection reveals this image was digitally altered to include the machinery. This tweet could be seen as an attempt to downplay the extent of damage resulting from a Russian-backed missile attack, and in a wider context to create confusion and doubt as to veracity of other images emerging from the conflict zone.
Journalists and fact-checkers are also working to verify content and raise awareness of known fakes. Large, well-resourced news outlets such as the BBC are also calling out misinformation.
Social media platforms have added new labels to identify state-run media organisations or provide more background information about sources or people in your networks who have also shared a particular story.
They have also tweaked their algorithms to change what content is amplified and have hired staff to spot and flag misleading content. Platforms are also doing some work behind the scenes to detect and publicly share information on state-linked information operations.
What Can I Do about It?
You can attempt to fact-check images for yourself rather than taking them at face value. An article we wrote late last year for the Australian Associated Press explains the fact-checking process at each stage: image creation, editing and distribution.
Here are five simple steps you can take:
Examine the metadata
This Telegram post claims Polish-speaking saboteurs attacked a sewage facility in an attempt to place a tank of chlorine for a “false flag” attack.
But the video’s metadata—the details about how and when the video was created—show it was filmed days before the alleged date of the incident.
To check metadata for yourself, you can download the file and use software such as Adobe Photoshop or Bridge to examine it. Online metadata viewers also exist that allow you to check by using the image’s web link.
One hurdle to this approach is that social media platforms such as Facebook and Twitter often strip the metadata from photos and videos when they are uploaded to their sites. In these cases, you can try requesting the original file or consulting fact-checking websites to see whether they have already verified or debunked the footage in question.
If old content has been recycled and repurposed, you may be able to find the same footage used elsewhere. You can use Google Images or TinEye to “reverse image search” a picture and see where else it appears online.
But be aware that simple edits such as reversing the left-right orientation of an image can fool search engines and make them think the flipped image is new.
Look for inconsistencies
Does the purported time of day match the direction of light you would expect at that time, for example? Do watches or clocks visible in the image correspond to the alleged timeline claimed?
You can also compare other data points, such as politicians’ schedules or verified sightings, Google Earth vision or Google Maps imagery, to try and triangulate claims and see whether the details are consistent.
Ask yourself some simple questions
Do you know where, when and why the photo or video was made? Do you know who made it, and whether what you’re looking at is the original version?
Using online tools such as InVID or Forensically can potentially help answer some of these questions. Or you might like to refer to this list of 20 questions you can use to “interrogate” social media footage with the right level of healthy skepticism.
Ultimately, if you’re in doubt, don’t share or repeat claims that haven’t been published by a reputable source such as an international news organization. And consider using some of these principles when deciding which sources to trust.
By doing this, you can help limit the influence of misinformation, and help clarify the true situation in Ukraine.
A neural network that teaches itself the laws of physics could help to solve some of physics’ deepest questions. But first it has to start with the basics, just like the rest of us. The algorithm has worked out that it should place the Sun at the centre of the Solar System, based on how movements of the Sun and Mars appear from Earth.
The machine-learning system differs from others because it’s not a black that spits out a result based on reasoning that’s almost impossible to unpick. Instead, researchers designed a kind of ‘lobotomized’ neural network that is split into two halves and joined by just a handful of connections. That forces the learning half to simplify its findings before handing them over to the half that makes and tests new predictions.
A long-awaited experimental result has found the proton to be about 5% smaller than the previously accepted value. The finding seems to spell the end of the ‘protonradius puzzle’: the measurements disagreed if you probed the proton with ordinary hydrogen, or with exotichydrogen built out of muons instead of electrons. But solving the mystery will be bittersweet: some scientists had hoped the difference might have indicated exciting new physics behind how electrons and muons behave.
This week is a special one for all of us at Nature: it’s 150 years since our first issue, published in November 1869. We’ve been working for well over a year on the delights of our anniversary issue, which you can explore in full online.
A century and a half has seen momentous changes in science, and Nature has changed along with it in many ways, says an Editorial in the anniversary edition. But in other respects, Nature now is just the same as it was at the start: it will continue in its mission to stand up for research, serve the global research community and communicate the results of science around the world.
Nature creative director Kelly Krause takes you on a tour of the archive to enjoy some of the journal’s most iconic covers, each of which speaks to how science itself has evolved. Plus, she touches on those that didn’t quite hit the mark, such as an occasion of “Photoshop malfeasance” that led to Dolly the sheep sporting the wrong leg.
Scientific glassblower Terri Adams uses fire and heavy machinery to hand-craft delicate scientific glass apparatus. “My workbench hosts an array of tools for working with glass, many of which were custom-made for specific jobs,” says Adams. “Each tool reminds me of what I first used it for and makes me consider how I might use it again.” (Leonora Saunders for Nature)
(If you have recommended people before and you want them to count, please ask them to email me with your details and I will make it happen!) Your feedback, as always, is very welcome at briefing@nature.com.
