Tag Archives: Probability

Understanding Probability: Common Misconceptions Explained

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Language and Probability

The Language of Probability: Clarity is Key.

Makhbubakorn Ismatova/Getty Images

When someone states they are “probably” having pasta for dinner but later opts for pizza, do you find it surprising or consider them dishonest? On a more critical note, what does it imply when the United Nations asserts it is “very likely” that global temperatures will rise by over 1.5 degrees Celsius in the next decade, as reported last year? The translation between the nuances of language and the intricacies of mathematical probability can often seem challenging, yet we can discover scientific clarity through careful analysis.

Two fundamental points about probability are widely accepted: Something labeled “impossible” has a 0% chance of occurrence, while a “certain” event carries a 100% likelihood. However, confusion arises in between these extremes. Ancient Greeks, including Aristotle, differentiated between terms such as Eikos, meaning the most likely, and Pitanon, which signifies plausible. This presents challenges: persuasive rhetoric may not always align with likelihood. Additionally, both terms were translated by Cicero into the modern term probability.

The concept of a measurable mathematical approach to probability emerged significantly later, primarily in the mid-17th century during the Enlightenment. Mathematicians began to address gambling dilemmas, such as equitable distribution of winnings during interruptions. Concurrently, philosophers probed whether it was feasible to quantify varying levels of belief.

For instance, in 1690, John Locke categorized degrees of probability on a spectrum from complete certainty to confidence based on personal experience, down to testimony affected by repetition. This classification remains vital in legal contexts, both historically and presently.

The interplay between law and probability persisted among philosophers. In his writings of the mid-19th century, Jeremy Bentham criticized the inadequacy of common language in expressing evidence strength. He proposed a numerical ranking system to gauge belief strength, but ultimately deemed its subjectivity as impractical for justice.

A century later, economist John Maynard Keynes rejected Bentham’s certainty measure in favor of relational approaches. He argued that it was more effective to discuss how one probability might exceed another, focusing on the knowledge base for these estimations, thus establishing a hierarchy without offering systematic communication methods for terms such as “may” or “likely.”

Interestingly, the first systematic resolution to this challenge did not arise from mathematicians or philosophers but from a CIA intelligence analyst named Sherman Kent. In 1964, he introduced the idea of estimating probability with specific terminology for National Intelligence Estimates designed to guide policymakers. He articulated the dilemma faced by “poets,” who articulate meaning through words, versus “mathematicians,” who advocate for exact figures. Kent initiated the idea that specific words correspond to precise probabilities, designating “virtually certain” as a 93% probability, but also allowing some leeway to accommodate differing interpretations.

This framework for understanding probability transitioned from the intelligence sector to scientific applications. A review of recent research dating back to 1989 explored how both patients and medical professionals interpret terms like “may” in medical scenarios. The findings showed some alignment with Kent’s framework, although with distinctions.

Returning to the original question about the meaning of “very likely” regarding climate change, the Intergovernmental Panel on Climate Change (IPCC) offers clarity with explicit definitions. According to their guidance, “very likely” signifies a 90% to 100% probability of an event’s occurrence. Alarmingly, many climate scientists now assert that temperatures have already surpassed the critical threshold of 1.5 degrees Celsius.

However, situations are rarely straightforward. Logically, the statements “Event A is likely to occur” and “Event A is unlikely to be avoided” should correlate, albeit research published last year reveals that labeling a climate forecast as “unlikely” diminishes perceived evidence strength and consensus among scientists compared to stating it’s “likely.” This cognitive bias might stem from a preference for positive framing over negative alternatives. A classic example includes a community of 600 individuals facing a health crisis; when presented with two treatment options, most favor one that saves 200 lives over one that saves 400, even if both are statistically similar.

So, what lessons can we draw from this exploration? Firstly, quantifiable data effectively enhances communication of uncertainty. If numerical specificity isn’t available, stating, “75% of the time, I plan to have pasta for dinner,” may raise eyebrows. In such instances, ensure shared understanding of terminology, even in the absence of a formalized framework like Kent’s. Lastly, accentuating the positive tends to foster acceptance of predictions. How likely is that? Well, that’s hard to quantify.

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Source: www.newscientist.com

Probability of Asteroid 2024 YR4 Impacting the Moon May Increase to 30%

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Asteroid 2024 YR4 might strike the moon

Mark Garlick/Science Photo Library

Astronomers have a limited timeframe to determine if they will intervene to stop asteroid 2024 YR4 from colliding with the moon in 2032. A brief observation period utilizing the James Webb Space Telescope is set to commence in February, as new findings indicate that the potential for impact is rising to over 30%, posing a significant threat to satellites and future lunar infrastructures.

Discovered late last year, 2024 YR4 quickly emerged as the most probable asteroid to strike Earth. The worst-case scenario initially estimated a collision probability of 1 in 32 for 2032. However, further observations have nearly eliminated the chance of an Earth impact, leaving a 4 percent possibility of a collision with the moon, which could endanger numerous vital satellites orbiting Earth due to debris.

Despite the considerable risk associated with this asteroid, space agencies have yet to take action, although NASA researchers are exploring potential deflection strategies, such as deploying a nuclear charge near the asteroid.

The asteroid has recently moved out of range for Earth’s telescopes, limiting astronomers’ ability to obtain further data on its orbit until it reappears in 2028, which may not allow enough time to execute a deflection mission.

Fortunately, the James Webb Space Telescope (JWST) anticipates a brief operational window to observe the asteroid in February 2026 and again in April 2024, offering a critical opportunity to plan a deflection mission. Andrew Rivkin from Johns Hopkins University in Maryland remarked, “By 2028, it will be in close proximity, so capturing data in early 2026 grants us additional time.”

This advantageous positioning will enable JWST to observe 2024 YR4, which follows a distinct orbit around Earth, undetectable by other ground-based telescopes, but the observation will still be challenging, as the asteroid is expected to be dim, even for JWST’s highly sensitive instruments. There will be two narrow windows for observation on February 18th and 26th.

Rivkin and his team computed how new data regarding the asteroid’s positions and velocities could alter the existing understanding based on these observations. Their findings indicate an 80% likelihood of reducing the probability of a lunar impact to under 1%, while there is a 5% chance that the risk could increase to 30% or higher. JWST should have a chance to repeat these observations in 2027, but this will provide less time for decision-making, according to Rivkin.

Nonetheless, it remains uncertain whether space agencies would opt to plan missions in the event of increased risks. “The question of whether planetary defense extends to the moon is entirely new, and different agencies may have varied responses,” Rivkin noted. “If a company operates many satellites, they might advocate for a particular course of action.”

Richard Moisle from the European Space Agency indicated that while the current budget does not allocate for deflection or reconnaissance missions regarding the asteroid, they will reevaluate if next year’s observations indicate a heightened risk of collision. “We chose to delay our decision until next year to allow for a thorough evaluation of our options,” Moisle stated.

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Source: www.newscientist.com

The evolving probability of asteroids striking Earth in 2032

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Asteroids flying near Earth in 2032 are expected to safely pass through the planet, with a shock chance of just 0.004%. NASA said Monday.

This is a significant downgrade to the risk from the record highs the space agency gave earlier last week.

The asteroid known as the 2024 YR4 is between 130 and 300 feet wide and is large enough to cause local damage if it hits Earth. However, the exact odds of the event have been an impressive target since the space rock was first detected about two months ago.

The extremely slim chances NASA estimated on Monday were even smaller than the 0.28% chance it gave late last week. Just a few days ago, the agency had the chance to 1.5% and 3.1% before that.

With the short odds exceeded 3%, the first object officially classified as Level 3 of 10 out of 10 in a measurement known as the Torino Scale became the space rock. Richard Binzel first proposed it nearly 30 years ago.

Level 3 classification means that objects are worthy of attention by astronomers, and pose a threat of “close encounters.”

Named after an Italian city officially adopted by astronomers In 1999, the Turin Impact Hazard Scale is a way to communicate to the public the risks posed by asteroids and other space objects near Earth to planets.

The scale is color-coded, with categories ranging from 0 (white without risk) to 10 (red for a particular collision). With a 3.1% chance of colliding with the Earth, 024-year-old 4 was temporarily placed in the mid-yellow zone of the scale.

The gusts of news reports about the asteroids have attracted more attention than ever on Turin's scale. Binzel said this type of situation was exactly why he created the system in the first place.

“The Massachusetts Institute of Technology has made it a great opportunity to learn about the world,” said Bindel, a professor of planetary science at the Massachusetts Institute of Technology. “But it's like being between a rock and a difficult place because we want to report what we know to maintain the trust of our people, but we don't want to raise unnecessary anxiety. Because.”

The challenges of walking that thin line are revealed in Asteroid 2024 YR4.

According to NASA, the reason for the recent decline in impact probability is The ground telescope was able to get a better look Based on these observations, on the Space Lock on February 19th and 20th, astronomers were able to improve models of asteroid orbits, allowing them to estimate the Space Lock trajectory more accurately. This will help scientists to more reliably predict where 2024 YR4 will be on December 22, 2032, where asteroids are likely to encounter closely with Earth.

The shifting probability is somewhat dizzy, but according to Bindsel, the possibility that such a close-Earth asteroid could dance like this is completely normal.

The Asteroid 2024 YR4 is thought to measure up to 300 feet in diameter.Atlas

When Binzel debuted the Turin scale in the astronomical community decades ago, his goal was to promote greater public awareness of shock risk. According to him, the idea was to implement something similar to the Richter scale, which measures the magnitude of an earthquake, or the Saffir Simpson scale, which assigns categories to hurricanes based on wind speed.

But when he first presented the system at the 1997 UN conference, it wasn’t well received, he said. According to Biinsel, some astronomers were skeptical that it would help the public.

In the same year, scientists discovered an asteroid called XF11 in 1997. We thought this could hit Earth in 2028. It didn’t take long for astronomers to eliminate potential conflicts, but the ending story expanded in news reports, followed by subsequent denunciations. Something that was perceived as a major mistake.

“It ended up being a bit of embarrassment,” Binzel said. “Astronomers did not make any errors, but there was no good way to convey uncertainty. So this classifies objects that cannot be immediately ruled out over centuries of Earth. This motivated me to propose a simple system for

Binzel once again presented the scale in Turin at a conference held in Turin in 1999, attended by representatives from the NASA and the European Space Agency. In that workshop, the system was ultimately adopted by the International Astronomical Union, a non-governmental organization made up of professional astronomers who act like the governing body of the astronomical community.

In addition to using colours and numbers to accommodate different risk levels, the scale includes explanations of potential outcomes, the possibility of changing risk assessments, and actions that the government or the public should take.

For example, the level 6 threat in the orange zone explains the possibility of close shaving by “large objects pose a serious and uncertain threat of a global catastrophe.”

Astronomers recommend giving this object “critical attention” to know if a collision occurs. “If the encounter is less than 30 years, the government's emergency plan could be guaranteed,” the scale states.

On the other hand, Level 3 threat, according to the scale explanation, means that “current calculations provide more than 1% chance of a collision that can be locally destructive.” “Perhaps observations of the new telescope lead to reallocation to level 0. Attention by civil servants is valuable if the encounter is within ten years.”

Naturally, Binzel was correctly suspected when asteroid 2024 YR4 was considered to be the 3 that would eventually be downgraded.

Meanwhile, however, the 2024 YR4 hit an unpleasant milestone. It is the only known astide with a classification above level 1, and set the record to reach the highest impact probability and spend the longest time with the probability above 1%. According to the European Space Agency.

The higher classification of similar or larger sized asteroids on the Turin scale is in 2004, when asteroid Apophis was temporarily ranked as Level 4, with an estimated 2.7% chance of hitting Earth There was a possibility.

Vincell said he was pleased to witness the scale feature in real time, but he is pleased to be modest about his connection to it.

“At the end of the day, if Turin scale helps, there's a great deal of satisfaction. It really makes my day,” he said. “But it's nice to hide my name behind where the scale was adopted. It helps to keep my phone from ringing too much.”

Source: www.nbcnews.com

There is a high probability that Asteroid 2024 YR4 will not collide with Earth in 2032.

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Astronomers raced to observe asteroid 2024 YR4

NASA/Magdalena Ridge 2.4M Telescope/New Mexico Institute of Technology/Ryan

The world’s space agency has reduced the chance that asteroid 2024 YR4 will affect Earth by less than 1%. This strongly suggests that potentially catastrophic conflicts will be avoided. However, the asteroid probably passes very extraordinarily close to our planet, giving astronomers a rare opportunity to observe the asteroid in close proximity.

“We don’t expect the impact probability above 1% will exceed 1% in 2032 due to our close approach with the Earth,” he says. Richard Moisle With the European Space Agency (ESA). “The most likely further development is a further reduction in impact probability, perhaps even dropping to zero.”

The alarm last December regarding the asteroid 2024 YR4 was first raised in December last year, when it discovered it could be on Earth’s collision course in 2032. It looks like it’s 40-90 meters wide and can produce a fatal explosion if attacked by a city. Over the next few weeks, global telescopes and space agencies have closely tracked their orbits, honing their future paths more accurately. On February 17th, we reached our highest shock risk with one in 32nd chance, but in the next few days this reduced to a 67th or 1.5% risk.

On February 20th, new observations led to a sudden downgrade of this risk, with NASA having a 0.27% impact chance of 1-in-360, and ESA having a 0.16%, or 1-in-in-in- in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in- in-ine 625. These ratings placed it at 1 on a 10-point Turin scale used to evaluate the hazards brought about by such objects. That score has decreased from 3. So, 2024 YR4 is now considered one of many low-risk asteroids discovered each year, but ultimately misses Earth.

I say this is good news Gareth Collins At Imperial College in London, asteroids still serve as a dry run for planetary defense systems and scientific purposes. “This still makes for an epic, close approach. If the risk of a hit was so high, it must be close to us,” he says.

Space companies that were sketching possible schemes to deflect NASA, ESA and asteroids, say they will likely continue their plans. Niklas Voight At OHB, a German space company. Voigt and his team were beginning to think about the mission to deflect the 2024 YR4, but the new risks won’t change that, he says. “The risk has decreased, but for the time being, we are still working on the topic.”

A close approach could be a good opportunity to test its ability to deflect asteroids, says Voigt – the only previous attempt to do this was NASA’s DART mission, the 160m in 2022 The asteroid-shaped trajectory of the . Satellites can be constructed to send to the 2024 YR4, he says, as well as the ESA’s Ramses satellite, to travel to observe the asteroid Apophis, passing near Earth in 2029. It is set to do so.

The final decision on what to do about YR4 2024 will likely not be made until the planned observation in March using James Webb Space Telescope. Not only does it collect orbital data, it also helps to better assess the size and composition of the asteroid. That information will be provided to the UN Assisted Space Mission Planning Advisory Group, which will determine the best action around the end of April. “These are very useful exercises to find a pinch point to make a decision, as you have time to do something wise in advance,” Collins says. “Absolutely, these committees are still meeting, but they’re probably less stressful.”

The possibility of an Earth shock has plummeted, but the risk of a YR4 collision with the moon in 2024 rose from 0.3% to 1.2%. “There’s a clear possibility that those numbers will rise even further,” says Moissl. “The exact impact of the effects of the moon from objects of this size is still under evaluation.”

The response to this object is also a useful rehearsal for other asteroids of concern, Collins says. “We want to avoid screams in the future, as the public is used to this threat, thinking, ‘Oh, that’s never going to happen.’ ”

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Source: www.newscientist.com