Posts Tagged ‘Science’
“Things that are so far removed from our daily experience… are inherently hard to understand”*…
That’s certainly true of numbers. And as the numbers grow, the cognitive challenges grow with them. (Indeed, by way of example: 1 million seconds, is roughly 11.5 days; 1 billion seconds is almost 32 years.)
We’ve looked before at the mysterious extremes of math: zero and infinity [and here]. But as Dan Falk reminds us, the numbers in between can seem pretty strange as well– especially the extremely large ones. In a review of Richard Elwes‘ Huge Numbers: A Story of Counting Ambitiously, From 4½ to Fish 7, Falk spotlights some of the largest numbers humans have ever contemplated…
… Aficionados of huge numbers are called “googologists,” a reference to the number 10100, known as a googol. Such numbers have a peculiar sort of existence. For the vast majority of us, they’re of limited everyday value. Calculations at the supermarket checkout, or at tax time in April, typically involve far more modest figures. Perhaps we’ve read that the U.S. national debt is in excess of $38 trillion — a mind-numbing figure, to be sure, but it’s not as though any one individual needs to count it up in stacks of $20 bills.
And yet, much larger numbers await those who seek them out. Consider the kinds of numbers that crop up in problems involving combinations and permutations. For example, in how many distinct ways can one shuffle a deck of cards? Elwes takes us through the calculation, and we end up with a figure of about 8×1067. Compared to that number, the odds of getting a royal flush when dealt a five-card poker hand seem pretty decent, sitting at a mere 1 in 649,740 (still rare enough that many poker players have never held such a hand). Or consider that famous 1980s cultural touchstone, the Rubik’s cube. In how many ways can one scramble the cube? It turns out that the figure is about 43 quintillion, or 4.3×1019 — but in spite of that ridiculously large figure, people do routinely solve the puzzle, and champions can do it in mere seconds. In fact, as Elwes explains, no Rubik’s cube arrangement is more than 20 moves away from any other arrangement.
Or consider the age of the universe, estimated to be about 13.8 billion years. This may seem like a lengthy span of time, but our cosmic future is where the really big numbers come up. Elwes examines the so-called heat death of the universe, in which all matter has broken down into subatomic particles. We may reach this point in [10 raised to the 10th power, raised again to the 120th power] years — this dizzying figure is 10 raised to the power of 10120 — at which point, Elwes says, the universe will have ballooned up to a diameter of 10 to the power of 10 to the power of 10120 light years. (Yes, that’s [10 raised to the 10th power, again to the 10th power, then to the 120th power] light years.) Elwes adds a footnote: “At this point, the choice of units hardly matters; the distance is so immense that whether we choose to measure it in Planck lengths or giga-light years makes little difference.” Let that sink in!
As mind numbing as such figures are, the highest numbers contemplated by humans come not from physics but from pure mathematics and computer science. Like “Graham’s number” — an immense figure put forward as the upper-bound for solutions to a problem in a branch of mathematics known as Ramsey theory. Some readers may find the ensuing discussion of multi-dimensional hypercubes a bit challenging, but one can enjoy the payoff regardless: We end up with a number that can’t even be expressed in conventional notation, and which earned a mention in the 1980 edition of the “Guinness Book of World Records” as “the highest number ever used in a mathematical proof.”
Reading this book is a little bit like sitting in the back row of an auction house where a rare Picasso (let’s say) is up for grabs: How high is this thing going to go? And indeed, Elwes keeps going. We eventually meet the so-called busy beaver numbers, a set of numbers that crop up in theoretical computer science, when one tries to deduce whether a particular computer program will eventually stop, or keep going forever — a conundrum known as the “halting problem.” As Elwes explains, it’s not at all straightforward to distinguish the two types of programs (and if it was, it would help mathematicians tackle some of the most vexing problems in their field).
The fifth busy beaver number, known as BB(5) — associated with a computer program that can access five internal states — works out to 47,176,870. And that’s as far as we’ve gotten, Elwes explains. No one has worked out the value of BB(6), but he assures us that it’s beyond the range of any physical computer; and BB(16) leaves even Graham’s number in the dust.
But wait, there’s more! “Rayo’s number,” concocted by Agustín Rayo — a dean and professor at MIT — using set theory, is bigger still (here’s a fun video about it); and “Fish 7,” mentioned in the book’s subtitle, named for a Japanese googologist who goes by the pseudonym “Fish,” builds on Rayo’s number, and … well, the details are not easily digested, but the mind-melting nature of these numbers comes across as a feature, not a bug, of Elwes’s story… the narrative is enlivened by explorations of the peculiarities of math history…
… Archimedes tried to estimate how many grains of sand would be needed to fill up the known universe, back in the third century B.C. Did he simply have too much time on his hands? Not at all, insists Elwes: The Greek thinker was articulating an important idea — that no matter how unfathomably large a quantity may be, we can describe it with precision, thanks to mathematics. “Archimedes,” he writes, “was penning a manifesto for the expressive power of large numbers.”…
… [Elwes focuses] on numbers that are ridiculously large and yet finite. In the end, perhaps this is the most mind-boggling fact of all: that these enormous numbers, from Graham’s number to Fish 7 and beyond, fall as far short of infinity as does the humble number 1…
The mysteries of the massive: “The Mind-Boggling Science of Enormous Numbers,” @danfalk.bsky.social on @richardelwes.bsky.social in @undark.org.
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As we enumerate enormity, we might spare a thought for a seminal mathematician, Alan Turing; he died on this date in 1954. He was a foundational computer science pioneer (inventor of the Turing Machine (an influential model for the general-purpose computer), creator of the “Turing Test” (only too relevant in these AI-infected times), inspiration for “The Turing Award” (the “Nobel Prize of computing“), and cryptographer (leading member of the team that cracked the Enigma code during WWII).
“Here comes the sun”*…
Further, in a fashion, to last Wednesday’s post… We’ve looked before (e.g., here) at the potential havoc that solar storms could wreak on our electified lives. Now, as Paul Voosen reports, scientists are speculating on a defense, suggesting that gases released from satellites could slash the threat of severe “space weather”…
When violent eruptions from the Sun slam into Earth’s magnetic field, they do more than paint aurorae across the night sky. They can scramble the electronics of satellites and induce powerful ground currents that knock out electrical grids. It’s been estimated that a one-in-a-100-year solar storm like the 1859 Carrington Event could cause more than $3 trillion of damage to the power grid alone. [See here.]
Yet for decades, society’s only defenses have been better space weather forecasts and more durable technology on the ground and in space. Now, a small group of space physicists says humanity should intervene and weaken solar storms in real time. In a study published [recently] in Space Weather, the researchers describe a provocative proposal called “StormWall”: a fleet of satellites that would release hundreds of tons of gases into space just before a solar storm strikes Earth. Computer simulations suggest the artificial cloud could cut the intensity of a major solar storm by half or more. “It’s as if you could install an airbag in the magnetosphere,” says Daniel Welling, a co-author and space physicist at the University of Michigan.
Call it “helioengineering”—a deliberate intervention in the near-Earth space environment. But unlike controversial geoengineering proposals to mitigate global warming, which would inject long-lived Sun-blocking particles into the atmosphere, StormWall’s protective gases would dissipate within hours, says Brian Walsh, the study’s lead author and a space physicist at Boston University. “It’s waiting for us to do some temporary modification.”
The proposal would require more extensive simulations and testing. But it is “highly innovative and appears to be quite feasible in the near term,” says Allison Jaynes, a space physicist at the University of Iowa. It’s a “laudable idea,” adds Gurudas Ganguli, a space physicist at the U.S. Naval Research Laboratory (NRL)…
[Voosen explains the technology proposed and considers the challenges in its implementation…]
… Of course, like an airbag, StormWall would have to be replaced if deployed. But just as NASA and other space agencies are studying how to protect the planet from asteroids [and here], Walsh says there’s a good argument for fortifying an electronics-dependent society against massive solar eruptions. “If we lose all our power grids and can’t use the internet for 6 years, it would be traumatic.”
“Radical proposal would block solar storms with orbital ‘airbag’” from @science.org.
* George Harrison
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As we apply sunscreen, we might send bright birthday greetings to Godfried Wendelen; he was born on this date in 1580. And astronomer (and Catholic priest) known as “the Ptolemy of his time.” Despite the tenets of his church, Wendelen was an audacious proponent of the Copernican theory that the planets orbit around the sun. He made more accurate measurements of the distance to the sun than those previously made by Aristachus (2,000 years earlier) from the geometrical relationships at the exact time of a half-moon.
Wendelen is considered by many as a precursor of Kepler and Newton, and was in fact cited by Newton in his Principia. The crater Vendelinus on the Moon is named after him
“A simile is just a metaphor with the scaffolding still up”*…
Russell Samora has been fooling around with figures of speech; with his colleagues at The Pudding, he’s fielded a fascinating analysis of of that comparative workhorse, the simile…
Similes are all around us. But, if you haven’t considered this figure of speech since grade school, here’s a refresher: similes compare a shared quality of two things, often using “like” or “as.”
I pulled every simile in the form “as ___ as ___” from tens of thousands of fiction books for the top 500 most common adjectives… I thought it would be a trivial exercise, but the more I poked around, the more questions I had…
Samora explains how similes are structured and how they are used (and with what relative frequency) in literature. He examines some of the most common– and several special cases (“The Ironic Ones”). And he explains his methodology and sources… all in the context of a lovely interactive data visualization.
It’s as cool as hell: “Comparisons as Predictable as the Sunrise,” from @pudding.cool.
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As we agree with Steve Martin that “a day without sunshine is like, you know, night,” we might recall that it was on this date in 1789 that Richard Kirwan published his essay in support of the phlogiston theory (the belief, that dates to alchemical times, in the existence of a fire-like element (dubbed “phlogiston”) contained within combustible bodies and released during burning. Kirwan was among the last of its advocates.
A well-regarded scientist in the late 18th and early 19th centuries, Kirwan met and corresponded with Black, Lavoisier, Priestley, and Cavendish. Indeed, while scientific history remembers him as a defender of an incorrect theory, his work probably spurred Priestley and Lavoisier, who respectively discovered and named the actual elemental agent of combustion, oxygen.
But Kirwan is also remembered for a personal eccentricity (one of many) that led to some referring to him (all too poignantly) as “crazy as a bed bug”: he hated bugs (especially flies). Kirwan paid his servants a bounty for each one they killed.
“Counterfactual reasoning, which deals with what-ifs, might strike some readers as unscientific. Indeed, empirical observation can never confirm or refute the answers to such questions.”*..
… still, we ask of our history, our reality “what if?”… The estimable Colin McGinn ponders why…
In a world with less gravity, the birds would be huge. In a world with more gravity, only insects would fly. In a world with more light and plant predators, plants would have consciousness and advanced intelligence. In a world with greater water resistance, whales would be small. In a colder world, there would be no cold-blooded animals. In a hotter world, all animals would be cold-blooded. In a wetter world, we would have gills. In a drier world, life would begin on the land, if it begins at all. In a world without tool-forming materials, we would still be walking on four legs. In a world with only predators, there would be no life. In a world without predators, life would be simple and boring. In a world without a sun, life would be primitive, unless there was another power source. In a world with available nuclear power, life would be much more abundant than now. In a world without consciousness, there would be no war. In a world without emotion, there would be no suicide. In a world with no psychology, there would be no madness. In a world without motion, there world be no progress and no death. In a world without causation, there would be only chaos. In a world without necessity, there would be only randomness. In a world without events, everything would be eternal. In a world without the infinite, there would be no finite. In a world without relations, there would be no facts. In a world without facts, there would be nothing. In a world without reality, there would be no unreality. In a world without nothingness, there would be no being.
Counterfactuals are inherently surprising, which is why we are fascinated by them. They tell us how different things could be under small changes. There are many kinds of counterfactual. We live in their shadow. They are always controversial, sometimes paradoxical. They give us a sense of intellectual freedom. They scare us. They are also funny. We wouldn’t know what to do without them. In a world without counterfactuals, there would be no thought worthy of the name…
On the utility– the necessity– of contemplating the unreal: “Counterfactuals.”
See also: “What is counterfactual thinking and why should you care about it?” (source of the image above)
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As we analyze alternatives, we might recall that it was on this date in 1898 that chemist Morris Travers discovered Krypton– the element (Kr), not the counterfactual planet.
“Adaptation and mitigation are two sides of the same coin. If mitigation is about preventing the unmanageable, adaptation is about managing the unavoidable.”*…
Adapting to climate change is quickly becoming part of everyday life. Nabig Chaudhry outlines seven trends we’re seeing for 2026 and beyond…
Within the climate and scientific communities, there’s growing concern about how quickly the world is approaching (and may exceed) 2°C of warming. 2024 was the first calendar year in which global average temperature exceeded 1.5°C above preindustrial levels. The impacts of rapid warming are becoming harder to miss: The climate is changing quickly almost everywhere, local and global climate risks are growing, progress on mitigation has become more politically constrained and uncertain, and many of our systems and policies aren’t prepared for the conditions ahead.
Growing climate risk is increasing the demand for new technologies, tools, strategies, and ways of thinking about climate adaptation. Since publishing our Insights on Climate Adaptation in 2025 report, the practice of climate adaptation has continued to develop, as more people, communities, organizations, and institutions work to understand and respond to climate risks.
People use different language to describe climate adaptation (including climate resilience), but the work centers on helping people, communities, and organizations manage the risks of a changing climate. Those activities are expanding, and we can already see signs. For example, new funding and investment vehicles are emerging, such as Tailwind Futures, and adaptation is receiving more dedicated space at major climate convenings, including The Adaptation Forum, a co-hosted gathering of thought leaders in the adaptation space during Climate Week NYC 2025.
In my role as Director of Climate Adaptation Research at Probable Futures and through my PhD program at the University of California, Berkeley, I speak with experts, read emerging research, and study adaptation developments every day. Through these conversations and insights, I’ve reflected on which adaptation trends are likely to emerge and strengthen…
Chaudhry npacks seven different trends; here, let me highlight two. The first is one that (Roughly) Daily has visited before, insurance…
Elevating insurance as a force in adaptation planning, policy, and behavior
Insurance is a valuable adaptation tool, as it can transfer risk, support recovery after climate shocks, and help signal where danger is increasing through premiums, deductibles, coverage limits, or insurer retreat. It can also shape incentives, because the way risk is priced can influence whether and how people and institutions reduce exposure, strengthen buildings, or avoid certain kinds of development.
As climate risks grow, damage to property and homes becomes more frequent and severe. Property owners are experiencing those shocks both physically (flooding, fire, wind damage, etc.) and financially as insurance markets adjust and recalibrate in response to changing probabilities and severities. Insurance markets have begun reflecting climate risk, and those changes are starting to influence where and how people build homes and infrastructure, where they invest in property, and where they choose to live.
A useful example of how insurance is beginning to influence adaptation efforts in the public sphere is Strengthen Alabama Homes, a program of the Alabama Department of Insurance. The program provides grants to help homeowners retrofit their homes and roofs to reduce wind damage from extreme winds and storms. Homeowners who participate can receive discounts on the wind portion of their homeowner’s insurance premium, which makes insurance not only a tool for recovery but also a tool for encouraging adaptation before exposure occurs.
Insurance pricing is one way climate risk is made visible, priced, and acted on through adaptation. I expect that insurance will increasingly influence adaptation planning, policy, and behavior, not only by helping people recover after climate shocks, but by shaping the choices people make before those shocks occur. The development of the insurance industry will therefore be an important factor in adaptation. If insurers become a source not only of risk pricing but also of risk information, adaptation guidance, and incentives to reduce risk, they could help more people act before losses occur. But that would require a meaningful shift in the role of insurance companies, from mainly pricing and transferring risk to also helping people reduce it…
The second goes to the contentious topic of geoengineering…
Expanding debate around the role of climate intervention
As warming continues, risks keep growing. We have more, clearer, worrisome signals that irreversible change, tipping points, and local climate changes so severe that adaptation is impractical if not impossible, are not far off. In response, people and institutions are starting new conversations about global-scale responses. One of those responses is climate intervention, sometimes called geoengineering.
Climate intervention generally refers to intentional efforts to alter Earth’s systems in order to counteract some of the effects of climate change. It can include approaches that remove carbon dioxide from the atmosphere, as well as approaches that reflect a portion of sunlight back into space, such as stratospheric aerosol injection.
Its relationship to adaptation is uneasy, but important. If climate intervention is, at its core, an effort to manage the otherwise unmanageable risks of global climate change, then is it another tool for adapting to climate change, or is it something fundamentally different? There is no consensus, and there may never be, not least because global action will cause uneven responses locally. We don’t know much about the potential impacts of some climate interventions, how they could affect different regions unequally, or what long-term consequences they may have for Earth’s climate and natural systems.
There are good reasons to have informed conversations and do fundamental research on intervention. People with adaptation expertise can help explore, illuminate, and explain what climate intervention could mean for society and nature. There are also likely to be benefits for adaptation professionals to participate in these conversations and research projects. Even if climate intervention is never widely deployed, the debate itself may shape adaptation thinking, climate policy, research funding, public trust, and international governance.
Climate change requires people to consider risks and options, whether for mitigation, adaptation, or intervention. Treating strategies for managing the rate, pace, and impacts of climate change as distinct and separate is unlikely to lead to good outcomes. I am hopeful that there will be more collaboration across these new fields as society faces new challenges that have a common root cause. This may include more discussion about how these technologies should be governed, whether they should receive more investment, and whether climate intervention is a possible third leg alongside mitigation and adaptation…
Eminently worth reading in full: “The near-term future of climate adaptation: emerging trends.”
* U. N. Environmental Program
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As we prepare, we might recall (wistfully) that it was on this date in 1942 that Bing Crosby, with the Trotter Orchestra and the Darby Singers, recorded Irving Berlin’s song, “White Christmas.” According to the Guinness Book of World Records, this version is the best-selling single of all time with an excess of 50 million copies sold worldwide. (In fact, the version most often heard today is not the original. After frequent use, the master had become damaged, so on March 18, 1947, Crosby re-recorded the holiday hit.)
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