Noymer and Carlton recommended keeping a six-foot distance during walks, though Marr thought being a little closer would be okay, so long as you’re walking side by side and not constantly turning to face each other.

People should be physically spaced out, so the number also depends on the size of the space you’re meeting up in.

The safest bubble, of course, is one that only includes you, but the people you live with are your de facto bubble-mates-meaning you get closer than six feet to one another, spend time indoors together, and break other rules that apply to interactions during a pandemic-and that’s fine.

“Part of the stay-at-home guidelines was essentially, ‘Your bubble should be your household,'” Carlton said, “And what we’re potentially shifting to is, ‘If you’re an extremely small household and really struggling with social isolation, it may be okay for you to have closer contact with a limited number of individuals.'” Restricting your bubble to just your household is still ideal, but Carlton said it’s “Probably not terrible” to carefully incorporate very limited others.

Keep in mind that each person you add to your bubble brings not only their own risks, but the risks of everyone else they may be exposed to.

So if you do add people to your bubble, choose them cautiously-but better to leave your bubble as is, if you can bear to.

“If you want to kiss somebody at the end of the date, that’s inadvisable-sorry,” Carlton said.

If you eventually end up starting a relationship, you’ll have to figure out when you’re comfortable becoming a part of each other’s bubble.

## Summary of “‘Anumeric’ People: What Happens When a Language Has No Words for Numbers?”

What’s more, the 7,000 or so languages that exist today vary dramatically in how they utilize numbers.

Speakers of anumeric, or numberless, languages offer a window into how the invention of numbers reshaped the human experience.

In my book, I explore the ways in which humans invented numbers, and how numbers subsequently played a critical role in other milestones, from the advent of agriculture to the genesis of writing.

While only a small portion of the world’s languages are anumeric or nearly anumeric, they demonstrate that number words are not a human universal.

Acquiring the exact meaning of number words is a painstaking process that takes children years.

That is, these smaller numbers are the basis of larger numbers.

Most number systems are the by-product of two key factors: the human capacity for language and our propensity for focusing on our hands and fingers.

Research on the language of numbers shows, more and more, that one of our species’ key characteristics is tremendous linguistic and cognitive diversity.

## Summary of “The Knapsack Problem in Computer Science Explained”

Researchers once took advantage of the problem’s complexity to create computer security systems, but these can now be cracked since the problem has been so well studied.

The knapsack problem belongs to a class of “NP” problems, which stands for “Nondeterministic polynomial time.” The name references how these problems force a computer to go through many steps to arrive at a solution, and the number increases dramatically based on the size of the inputs-for example, the inventory of items to choose from when stuffing a particular knapsack.

Some NP problems like the knapsack example have a special property: In the early 1970s, Stephen Cook and Richard Karp showed that a variety of NP problems could be converted into a single problem of formal logic.

One of the most stubborn questions in computer science and mathematics is whether these “NP” problems, including the knapsack problem, are truly different from “P” problems, those that can be solved in what is called polynomial time.

For this to work, a computer must also figure out whether any given number can be written as the sum of a subset of numbers in the private key, which becomes an easy knapsack problem.

Private information exchanges on today’s internet often use keys involving large prime numbers, and while factoring big numbers is difficult, it’s not thought to belong to the same “NP complete” class as the knapsack problem.

Beyond cryptography research, the knapsack problem and its NP complete cousins are everywhere in real life.

In small experiments in which participants were asked to fill a backpack on a computer screen with items carrying stated values and weights, people tended to have a harder time optimizing the backpack’s contents as the number of item options increased-the same problem computers have.

## Summary of “I Lived Through SARS and Reported on Ebola. These Are the Questions We Should Be Asking About Coronavirus.”

On Tuesday, after days of growing clamor to make more testing available, Vice President Mike Pence announced that the administration was issuing new guidance that “Will make it clear that any American can be tested” for COVID-19, the disease caused by the virus, and said that 2,500 kits would be sent out this week, an equivalent of 1.5 million tests.

Lifting restrictions on testing criteria is a much-needed step, but if your takeaway was that hundreds of thousands of Americans will be able to walk into doctors’ offices by Friday and immediately get tested, you’d be wrong.

At the end of the day, what I want to know is how many people can be tested.

As of Wednesday, the Association of Public Health Laboratories, which represents public health labs across the United States, told me that each CDC test kit can run about 700 specimens.

One hundred public labs received test kits from the CDC. When they’re all up and running, they’ll have a cumulative capacity of 10,000 samples a day.

A former FDA commissioner, Dr. Scott Gottlieb, told me that he’d like everyone with an influenza-like illness who tests negative for the flu to be able to get tested for COVID-19, which, given that we’re still in the midst of flu season, means a massive ramp-up would be required.

Under pressure to expand capacity, the FDA loosened restrictions on Saturday to allow academic hospital labs to start testing.

You know that’s because there’s not enough data, the denominator is pitifully small and we need to be testing a whole lot more people.

## Summary of “Why texting became such a powerful tool in the 2020 campaign”

Why texting became such a powerful tool in the 2020 campaign.

While younger voters may be more apt to get into longer exchanges via text, pretty much anybody under 50 will be comfortable enough with texting to respond to political texts coming in on their phones.

According to a study of texting in the 2018 midterms by the progressive digital advocacy group Tech for Campaigns, registered voters ages 26 and younger who were texted by a campaign turned out to vote 4% more often than voters who weren’t.

The Trump campaign has been working on its 2020 texting game since 2017, and plans to send “Almost a billion texts,” according to campaign manager Brad Parscale.

The Republican Party and the Trump campaign use a P2P texting platform called Opn Sesame which was developed by Gary Coby, who was an architect of the campaign’s winning digital strategy in 2016 and now leads the texting program for Trump 2020.

Whatever their source, the cell numbers can be queued up and placed into text messages in the P2P texting app, along with some boilerplate text that the sender can customize with their own words.

It did publish a 2016 advisory to political campaigns saying that only texts sent using an autodialer would be prohibited by the TCPA. In the absence of an official clarification, P2P texting lives on shaky regulatory ground, and campaign consultants are exploiting the loophole, fully aware that it might not last forever.

If P2P texts start to be used to spread such malicious content, consumers might stop opening them and regulators might take a new interest in P2P texting platforms.

## Summary of “Why Texans Don’t Want Any More Californians”

So if Californians aren’t moving more than in previous years, why are so many places suddenly freaking out about the influx of Golden Staters?

Western states taking in new Californians might be more anxious about change than they once were.

Texas, for example, has been the most popular destination for outbound Californians for more than a decade, consistently averaging about 60,000 to 70,000 new Golden Staters per year.

Now the state is at an inflection point, between its history as a ruby-red conservative stronghold and its future as a more mixed state with blue metros and red rural areas.

While California’s overall out-migration isn’t unprecedented, some states and counties are taking in an unprecedented share of newcomers from there.

The number of Californians moving to Idaho increased by 120 percent from 2012 to 2018.

San Francisco has the lowest percentage of children under 18 of any major city in the U.S., and Los Angeles County has seen a 17 percent decline in the number of kids in the past 10 years.

The state’s annual natural growth-births minus deaths-has plummeted from more than 300,000 in 2008 to 180,000 today.

## Summary of “Spies Are More Common, and Boring, Than You Think”

How many spies are there anyway? Many Americans were surprised in 2018 by allegations that a Russian woman, Mariia Butina, had infiltrated the National Rifle Association and was having sex with well-placed men, in the hopes of receiving information for Russia.

We think of spies as exotic, and so we imagine them as rare rather than commonplace.

Think about the bureaucratic side of spying.

In the account of Chinese spying in Silicon Valley, it was noted that the NIMBY movement that restricts construction and the resulting high rental prices are a major problem for the spies there.

That too suggests that most spies and potential spies lead a rather ordinary existence; they are not lavishly funded by their home governments.

If we look back at American history, whenever foreign spies were caught the reaction of the public was one of surprise or shock.

The McCarthy era in the 1950s seems to be the exceptional period when perhaps a large segment of the American public was overestimating the number of spies in the country and government.

John Negroponte, former director of national intelligence, admitted in 2006 that the U.S. was deploying about 100,000 spies around the world.

## Summary of “Math 101: A Reading List for Lifelong Learners”

“First published in 1930, this classic text traces the evolution of the concept of a number in clear, accessible prose. A Latvian mathematician who studied under Henri Poincare, Dantzig covers all the bases, from counting, negative numbers and fractions, to complex numbers, set theory, infinity and the link between math and time. Above all, he understood that the story of where mathematical ideas come from, how they relate to each other, and evolve over time, is key to a true appreciation of mathematics.”

“Pair Paulos with the just-released How Not to Be Wrong. Ellenberg deftly introduces the most basic mathematical tools in crisp, lively prose, liberally peppered with real-life examples, to help the reader start thinking like a mathematician. From Francis Galton and regression to the mean, to survivorship bias, uncertainty and the statistical challenges of ferreting out the signal from the noise in increasingly large data sets, he shows us how to use math to avoid potential pitfalls and make smart decisions.”

“The prose gets a bit turgid at times, and some readers might be deterred by the proofs and equations scattered throughout, but Berlinski has some lovely descriptions and turns of phrases. A unique take on a daunting subject, and a longtime favorite among math aficionados.”

Read These 3 Foundational Texts…One of the oldest surviving fragments of Euclid’s Elements, found at Oxyrhynchus and dated to circa AD 100.

First Six Books of the Elements of Euclid [full-text]Euclid, with annotations by John Casey.

When you’re ready to get your hands dirty with more formal instruction, I recommend perusing the extensive math catalogs of The Great Courses and Khan Academy.

Image via giphy.com and sciencefriday.com.

Opening with one of Russell’s public lectures in 1939, and featuring encounters with such historical luminaries as Kurt Gödel and David Hilbert, Papadimitriou’s narrative is inventive, thought-provoking and well worth reading for those interested in the nature of logic and the search for absolute truth.

## Summary of “Quanta Magazine”

For mathematicians and computer scientists, this was often a year of double takes and closer looks.

Some reexamined foundational principles, while others found shockingly simple proofs, new techniques or unexpected insights in long-standing problems.

Some of these advances have broad applications in physics and other scientific disciplines.

Others are purely for the sake of gaining new knowledge, with little to no known practical use at this time.

Quanta covered the decade-long effort to rid mathematics of the rigid equal sign and replace it with the more flexible concept of “Equivalence.” We also wrote about emerging ideas for a general theory of neural networks, which could give computer scientists a coveted theoretical basis to understand why deep learning algorithms have been so wildly successful.

Ordinary mathematical objects like matrices and networks yielded unexpected new insights in short, elegant proofs, and decades-old problems in number theory suddenly gave way to new solutions.

Mathematicians also learned more about how regularity and order arise from chaotic systems, random numbers and other seemingly messy arenas.

Like a steady drumbeat, machine learning continued to grow more powerful, altering the approach and scope of scientific research, while quantum computers hit a critical milestone.

## Summary of “Rubik’s Cube Algorithms”

A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies.

If you’re practicing and you want to scramble a solved cube, you have to keep the cube intact and scramble it up manually.

A cube that’s been broken and reassembled with its cubies randomly scrambled will have equal chances of being solvable to one of the following representatives.

There are(21212!) ways to put the cubies on the cube, but only one in 12 of those can be maneuvered to a solved cube.

You’ve now explored(21212!)/12, the number of cube configurations, which, to a mathematician studying the cube, is just preliminary.

Ernő Rubik made his first prototype in 1974, and early in the six years it took him to see it mass-produced, he was naturally the first person to ever solve the cube.

No matter how scrambled a cube gets, how few moves can be applied to solve it? If someone scrambled your cube using 500 moves, it’s certainly possible to unscramble it in fewer than 500 moves.

So no matter how scrambled a Rubik’s Cube looks, it’s always 20 moves away from solved.