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Shalitha Suranga

Shalitha Suranga

2 years ago

The Top 5 Mathematical Concepts Every Programmer Needs to Know

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Will Lockett

Will Lockett

2 years ago

The world will be changed by this molten salt battery.

Salt crystals — Pexels

Four times the energy density and a fraction of lithium-cost ion's

As the globe abandons fossil fuels, batteries become more important. EVs, solar, wind, tidal, wave, and even local energy grids will use them. We need a battery revolution since our present batteries are big, expensive, and detrimental to the environment. A recent publication describes a battery that solves these problems. But will it be enough?

Sodium-sulfur molten salt battery. It has existed for a long time and uses molten salt as an electrolyte (read more about molten salt batteries here). These batteries are cheaper, safer, and more environmentally friendly because they use less eco-damaging materials, are non-toxic, and are non-flammable.

Previous molten salt batteries used aluminium-sulphur chemistries, which had a low energy density and required high temperatures to keep the salt liquid. This one uses a revolutionary sodium-sulphur chemistry and a room-temperature-melting salt, making it more useful, affordable, and eco-friendly. To investigate this, researchers constructed a button-cell prototype and tested it.

First, the battery was 1,017 mAh/g. This battery is four times as energy dense as high-density lithium-ion batteries (250 mAh/g).

No one knows how much this battery would cost. A more expensive molten-salt battery costs $15 per kWh. Current lithium-ion batteries cost $132/kWh. If this new molten salt battery costs the same as present cells, it will be 90% cheaper.

This room-temperature molten salt battery could be utilized in an EV. Cold-weather heaters just need a modest backup battery.

The ultimate EV battery? If used in a Tesla Model S, you could install four times the capacity with no weight gain, offering a 1,620-mile range. This huge battery pack would cost less than Tesla's. This battery would nearly perfect EVs.

Or would it?

The battery's capacity declined by 50% after 1,000 charge cycles. This means that our hypothetical Model S would suffer this decline after 1.6 million miles, but for more cheap vehicles that use smaller packs, this would be too short. This test cell wasn't supposed to last long, so this is shocking. Future versions of this cell could be modified to live longer.

This affordable and eco-friendly cell is best employed as a grid-storage battery for renewable energy. Its safety and affordable price outweigh its short lifespan. Because this battery is made of easily accessible materials, it may be utilized to boost grid-storage capacity without causing supply chain concerns or EV battery prices to skyrocket.

Researchers are designing a bigger pouch cell (like those in phones and laptops) for this purpose. The battery revolution we need could be near. Let’s just hope it isn’t too late.

Stephen Moore

Stephen Moore

2 years ago

A Meta-Reversal: Zuckerberg's $71 Billion Loss 

The company's epidemic gains are gone.

Mid Journey: Prompt, ‘Mark Zuckerberg sad’

Mark Zuckerberg was in line behind Jeff Bezos and Bill Gates less than two years ago. His wealth soared to $142 billion. Facebook's shares reached $382 in September 2021.

What comes next is either the start of something truly innovative or the beginning of an epic rise and fall story.

In order to start over (and avoid Facebook's PR issues), he renamed the firm Meta. Along with the new logo, he announced a turn into unexplored territory, the Metaverse, as the next chapter for the internet after mobile. Or, Zuckerberg believed Facebook's death was near, so he decided to build a bigger, better, cooler ship. Then we saw his vision (read: dystopian nightmare) in a polished demo that showed Zuckerberg in a luxury home and on a spaceship with aliens. Initially, it looked entertaining. A problem was obvious, though. He might claim this was the future and show us using the Metaverse for business, play, and more, but when I took off my headset, I'd realize none of it was genuine.

The stock price is almost as low as January 2019, when Facebook was dealing with the aftermath of the Cambridge Analytica crisis.

Irony surrounded the technology's aim. Zuckerberg says the Metaverse connects people. Despite some potential uses, this is another step away from physical touch with people. Metaverse worlds can cause melancholy, addiction, and mental illness. But forget all the cool stuff you can't afford. (It may be too expensive online, too.)

Metaverse activity slowed for a while. In early February 2022, we got an earnings call update. Not good. Reality Labs lost $10 billion on Oculus and Zuckerberg's Metaverse. Zuckerberg expects losses to rise. Meta's value dropped 20% in 11 minutes after markets closed.

It was a sign of things to come.

The corporation has failed to create interest in Metaverse, and there is evidence the public has lost interest. Meta still relies on Facebook's ad revenue machine, which is also struggling. In July, the company announced a decrease in revenue and missed practically all its forecasts, ending a decade of exceptional growth and relentless revenue. They blamed a dismal advertising demand climate, and Apple's monitoring changes smashed Meta's ad model. Throw in whistleblowers, leaked data revealing the firm knows Instagram negatively affects teens' mental health, the current Capital Hill probe, and the fact TikTok is eating its breakfast, lunch, and dinner, and 2022 might be the corporation's worst year ever.

After a rocky start, tech saw unprecedented growth during the pandemic. It was a tech bubble and then some.

The gains reversed after the dust settled and stock markets adjusted. Meta's year-to-date decline is 60%. Apple Inc is down 14%, Amazon is down 26%, and Alphabet Inc is down 29%. At the time of writing, Facebook's stock price is almost as low as January 2019, when the Cambridge Analytica scandal broke. Zuckerberg owns 350 million Meta shares. This drop costs him $71 billion.

The company's problems are growing, and solutions won't be easy.

  • Facebook's period of unabated expansion and exorbitant ad revenue is ended, and the company's impact is dwindling as it continues to be the program that only your parents use. Because of the decreased ad spending and stagnant user growth, Zuckerberg will have less time to create his vision for the Metaverse because of the declining stock value and decreasing ad spending.

  • Instagram is progressively dying in its attempt to resemble TikTok, alienating its user base and further driving users away from Meta-products.

  • And now that the corporation has shifted its focus to the Metaverse, it is clear that, in its eagerness to improve its image, it fired the launch gun too early. You're fighting a lost battle when you announce an idea and then claim it won't happen for 10-15 years. When the idea is still years away from becoming a reality, the public is already starting to lose interest.

So, as I questioned earlier, is it the beginning of a technological revolution that will take this firm to stratospheric growth and success, or are we witnessing the end of Meta and Zuckerberg himself?

Clive Thompson

Clive Thompson

2 years ago

Small Pieces of Code That Revolutionized the World

Few sentences can have global significance.

Photo by Chris Ried on Unsplash

Ethan Zuckerman invented the pop-up commercial in 1997.

He was working for Tripod.com, an online service that let people make little web pages for free. Tripod offered advertising to make money. Advertisers didn't enjoy seeing their advertising next to filthy content, like a user's anal sex website.

Zuckerman's boss wanted a solution. Wasn't there a way to move the ads away from user-generated content?

When you visited a Tripod page, a pop-up ad page appeared. So, the ad isn't officially tied to any user page. It'd float onscreen.

Here’s the thing, though: Zuckerman’s bit of Javascript, that created the popup ad? It was incredibly short — a single line of code:

window.open('http://tripod.com/navbar.html'
"width=200, height=400, toolbar=no, scrollbars=no, resizable=no, target=_top");

Javascript tells the browser to open a 200-by-400-pixel window on top of any other open web pages, without a scrollbar or toolbar.

Simple yet harmful! Soon, commercial websites mimicked Zuckerman's concept, infesting the Internet with pop-up advertising. In the early 2000s, a coder for a download site told me that most of their revenue came from porn pop-up ads.

Pop-up advertising are everywhere. You despise them. Hopefully, your browser blocks them.

Zuckerman wrote a single line of code that made the world worse.

A photo of the cover of “You Are Not Expected To Understand This”; it is blue and lying on its side, with the spine facing the viewer. The editor’s name, Torie Bosch, is in a green monospaced font; the title is in a white monospaced font

I read Zuckerman's story in How 26 Lines of Code Changed the World. Torie Bosch compiled a humorous anthology of short writings about code that tipped the world.

Most of these samples are quite short. Pop-cultural preconceptions about coding say that important code is vast and expansive. Hollywood depicts programmers as blurs spouting out Niagaras of code. Google's success was formerly attributed to its 2 billion lines of code.

It's usually not true. Google's original breakthrough, the piece of code that propelled Google above its search-engine counterparts, was its PageRank algorithm, which determined a web page's value based on how many other pages connected to it and the quality of those connecting pages. People have written their own Python versions; it's only a few dozen lines.

Google's operations, like any large tech company's, comprise thousands of procedures. So their code base grows. The most impactful code can be brief.

The examples are fascinating and wide-ranging, so read the whole book (or give it to nerds as a present). Charlton McIlwain wrote a chapter on the police beat algorithm developed in the late 1960s to anticipate crime hotspots so law enforcement could dispatch more officers there. It created a racial feedback loop. Since poor Black neighborhoods were already overpoliced compared to white ones, the algorithm directed more policing there, resulting in more arrests, which convinced it to send more police; rinse and repeat.

Kelly Chudler's You Are Not Expected To Understand This depicts the police-beat algorithm.

About 25 lines of code that includes several mathematical formula. Alas, it’s hard to redact it in plain text here, since it uses mathematical notation

Even shorter code changed the world: the tracking pixel.

Lily Hay Newman's chapter on monitoring pixels says you probably interact with this code every day. It's a snippet of HTML that embeds a single tiny pixel in an email. Getting an email with a tracking code spies on me. As follows: My browser requests the single-pixel image as soon as I open the mail. My email sender checks to see if Clives browser has requested that pixel. My email sender can tell when I open it.

Adding a tracking pixel to an email is easy:

<img src="URL LINKING TO THE PIXEL ONLINE" width="0" height="0">

An older example: Ellen R. Stofan and Nick Partridge wrote a chapter on Apollo 11's lunar module bailout code. This bailout code operated on the lunar module's tiny on-board computer and was designed to prioritize: If the computer grew overloaded, it would discard all but the most vital work.

When the lunar module approached the moon, the computer became overloaded. The bailout code shut down anything non-essential to landing the module. It shut down certain lunar module display systems, scaring the astronauts. Module landed safely.

22-line code

POODOO    INHINT
    CA  Q
    TS  ALMCADR

    TC  BANKCALL
    CADR  VAC5STOR  # STORE ERASABLES FOR DEBUGGING PURPOSES.

    INDEX  ALMCADR
    CAF  0
ABORT2    TC  BORTENT

OCT77770  OCT  77770    # DONT MOVE
    CA  V37FLBIT  # IS AVERAGE G ON
    MASK  FLAGWRD7
    CCS  A
    TC  WHIMPER -1  # YES.  DONT DO POODOO.  DO BAILOUT.

    TC  DOWNFLAG
    ADRES  STATEFLG

    TC  DOWNFLAG
    ADRES  REINTFLG

    TC  DOWNFLAG
    ADRES  NODOFLAG

    TC  BANKCALL
    CADR  MR.KLEAN
    TC  WHIMPER

This fun book is worth reading.

I'm a contributor to the New York Times Magazine, Wired, and Mother Jones. I've also written Coders: The Making of a New Tribe and the Remaking of the World and Smarter Than You Think: How Technology is Changing Our Minds. Twitter and Instagram: @pomeranian99; Mastodon: @clive@saturation.social.

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Scott Galloway

Scott Galloway

2 years ago

First Health

ZERO GRACE/ZERO MALICE

Amazon's purchase of One Medical could speed up American healthcare

The U.S. healthcare industry is a 7-ton seal bleeding at sea. Predators are circling. Unearned margin: price increases relative to inflation without quality improvements. Amazon is the 11-foot megalodon with 7-inch teeth. Amazon is no longer circling... but attacking.

In 2020 dollars, per capita U.S. healthcare spending increased from $2,968 in 1980 to $12,531. The result is a massive industry with 13% of the nation's workers and a fifth of GDP.

Doctor No

In 40 years, healthcare has made progress. From 73.7 in 1980 to 78.8 in 2019, life expectancy rose (before Covid knocked it back down a bit). Pharmacological therapies have revolutionized, and genetic research is paying off. The financial return, improvement split by cost increases, is terrible. No country has expense rises like the U.S., and no one spends as much per capita as we do. Developed countries have longer life expectancies, healthier populations, and less economic hardship.

Two-thirds of U.S. personal bankruptcies are due to medical expenses and/or missed work. Mom or Dad getting cancer could bankrupt many middle-class American families. 40% of American adults delayed or skipped needed care due to cost. Every healthcare improvement seems to have a downside. Same pharmacological revolution that helped millions caused opioid epidemic. Our results are poor in many areas: The U.S. has a high infant mortality rate.

Healthcare is the second-worst retail industry in the country. Gas stations are #1. Imagine walking into a Best Buy to buy a TV and a Blue Shirt associate requests you fill out the same 14 pages of paperwork you filled out yesterday. Then you wait in a crowded room until they call you, 20 minutes after the scheduled appointment you were asked to arrive early for, to see the one person in the store who can talk to you about TVs, who has 10 minutes for you. The average emergency room wait time in New York is 6 hours and 10 minutes.

If it's bad for the customer, it's worse for the business. Physicians spend 27% of their time helping patients; 49% on EHRs. Documentation, order entry, billing, and inbox management. Spend a decade getting an M.D., then become a bureaucrat.

No industry better illustrates scale diseconomies. If we got the same return on healthcare spending as other countries, we'd all live to 100. We could spend less, live longer and healthier, and pay off the national debt in 15 years. U.S. healthcare is the worst ever.

What now? Competition is at the heart of capitalism, the worst system of its kind.

Priority Time

Amazon is buying One Medical for $3.9 billion. I think this deal will liberate society. Two years in, I think One Medical is great. When I got Covid, I pressed the One Medical symbol on my phone; a nurse practitioner prescribed Paxlovid and told me which pharmacies had it in stock.

Amazon enables the company's vision. One Medical's stock is down to $10 from $40 at the start of 2021. Last year, it lost $250 million and needs cash (Amazon has $60 billion). ONEM must grow. The service has 736,000 members. Half of U.S. households have Amazon Prime. Finally, delivery. One Medical is a digital health/physical office hybrid, but you must pick up medication at the pharmacy. Upgrade your Paxlovid delivery time after a remote consultation. Amazon's core competency means it'll happen. Healthcare speed and convenience will feel alien.

It's been a long, winding road to disruption. Amazon, JPMorgan, and Berkshire Hathaway formed Haven four years ago to provide better healthcare for their 1.5 million employees. It rocked healthcare stocks the morning of the press release, but folded in 2021.

Amazon Care is an employee-focused service. Home-delivered virtual health services and nurses. It's doing well, expanding nationwide, and providing healthcare for other companies. Hilton is Amazon Care's biggest customer. The acquisition of One Medical will bring 66 million Prime households capital, domain expertise, and billing infrastructure. Imagine:

"Alexa, I'm hot and my back hurts."

"Connecting you to a Prime doctor now."

Want to vs. Have to

I predicted Amazon entering healthcare years ago. Why? For the same reason Apple is getting into auto. Amazon's P/E is 56, double Walmart's. The corporation must add $250 billion in revenue over the next five years to retain its share price. White-label clothes or smart home products won't generate as much revenue. It must enter a huge market without scale, operational competence, and data skills.

Current Situation

Healthcare reform benefits both consumers and investors. In 2015, healthcare services had S&P 500-average multiples. The market is losing faith in public healthcare businesses' growth. Healthcare services have lower EV/EBITDA multiples than the S&P 500.

Amazon isn't the only prey-hunter. Walmart and Alibaba are starting pharmacies. Uber is developing medical transportation. Private markets invested $29 billion in telehealth last year, up 95% from 2020.

The pandemic accelerated telehealth, the immediate unlock. After the first positive Covid case in the U.S., services that had to be delivered in person shifted to Zoom... We lived. We grew. Video house calls continued after in-person visits were allowed. McKinsey estimates telehealth visits are 38 times pre-pandemic levels. Doctors adopted the technology, regulators loosened restrictions, and patients saved time. We're far from remote surgery, but many patient visits are unnecessary. A study of 40 million patients during lockdown found that for chronic disease patients, online visits didn't affect outcomes. This method of care will only improve.

Amazon's disruption will be significant and will inspire a flood of capital, startups, and consumer brands. Mark Cuban launched a pharmacy that eliminates middlemen in January. Outcome? A 90-day supply of acid-reflux medication costs $17. Medicare could have saved $3.6 billion by buying generic drugs from Cuban's pharmacy. Other apex predators will look at different limbs of the carcass for food. Nike could enter healthcare via orthopedics, acupuncture, and chiropractic. LVMH, L'Oréal, and Estée Lauder may launch global plastic surgery brands. Hilton and Four Seasons may open hospitals. Lennar and Pulte could build "Active Living" communities that Nana would leave feet first, avoiding the expense and tragedy of dying among strangers.

Risks

Privacy matters: HIV status is different from credit card and billing address. Most customers (60%) feel fine sharing personal health data via virtual technologies, though. Unavoidable. 85% of doctors believe data-sharing and interoperability will become the norm. Amazon is the most trusted tech company for handling personal data. Not Meta: Amazon.

What about antitrust, then?

Amazon should be required to spin off AWS and/or Amazon Fulfillment and banned from promoting its own products. It should be allowed to acquire hospitals. One Medical's $3.9 billion acquisition is a drop in the bucket compared to UnitedHealth's $498 billion market valuation.

Antitrust enforcement shouldn't assume some people/firms are good/bad. It should recognize that competition is good and focus on making markets more competitive in each deal. The FTC should force asset divestitures in e-commerce, digital marketing, and social media. These companies can also promote competition in a social ill.

U.S. healthcare makes us fat, depressed, and broke. Competition has produced massive value and prosperity across most of our economy.

Dear Amazon … bring it.

Greg Satell

Greg Satell

2 years ago

Focus: The Deadly Strategic Idea You've Never Heard Of (But Definitely Need To Know!

Photo by Shane on Unsplash

Steve Jobs' initial mission at Apple in 1997 was to destroy. He killed the Newton PDA and Macintosh clones. Apple stopped trying to please everyone under Jobs.

Afterward, there were few highly targeted moves. First, the pink iMac. Modest success. The iPod, iPhone, and iPad made Apple the world's most valuable firm. Each maneuver changed the company's center of gravity and won.

That's the idea behind Schwerpunkt, a German military term meaning "focus." Jobs didn't need to win everywhere, just where it mattered, so he focused Apple's resources on a few key goods. Finding your Schwerpunkt is more important than charts and analysis for excellent strategy.

Comparison of Relative Strength and Relative Weakness

The iPod, Apple's first major hit after Jobs' return, didn't damage Microsoft and the PC, but instead focused Apple's emphasis on a fledgling, fragmented market that generated "sucky" products. Apple couldn't have taken on the computer titans at this stage, yet it beat them.

The move into music players used Apple's particular capabilities, especially its ability to build simple, easy-to-use interfaces. Jobs' charisma and stature, along his understanding of intellectual property rights from Pixar, helped him build up iTunes store, which was a quagmire at the time.

In Good Strategy | Bad Strategy, management researcher Richard Rumelt argues that good strategy uses relative strength to counter relative weakness. To discover your main point, determine your abilities and where to effectively use them.

Steve Jobs did that at Apple. Microsoft and Dell, who controlled the computer sector at the time, couldn't enter the music player business. Both sought to produce iPod competitors but failed. Apple's iPod was nobody else's focus.

Finding The Center of Attention

In a military engagement, leaders decide where to focus their efforts by assessing commanders intent, the situation on the ground, the topography, and the enemy's posture on that terrain. Officers spend their careers learning about schwerpunkt.

Business executives must assess internal strengths including personnel, technology, and information, market context, competitive environment, and external partner ecosystems. Steve Jobs was a master at analyzing forces when he returned to Apple.

He believed Apple could integrate technology and design for the iPod and that the digital music player industry sucked. By analyzing competitors' products, he was convinced he could produce a smash by putting 1000 tunes in my pocket.

The only difficulty was there wasn't the necessary technology. External ecosystems were needed. On a trip to Japan to meet with suppliers, a Toshiba engineer claimed the company had produced a tiny memory drive approximately the size of a silver dollar.

Jobs knew the memory drive was his focus. He wrote a $10 million cheque and acquired exclusive technical rights. For a time, none of his competitors would be able to recreate his iPod with the 1000 songs in my pocket.

How to Enter the OODA Loop

John Boyd invented the OODA loop as a pilot to better his own decision-making. First OBSERVE your surroundings, then ORIENT that information using previous knowledge and experiences. Then you DECIDE and ACT, which changes the circumstance you must observe, orient, decide, and act on.

Steve Jobs used the OODA loop to decide to give Toshiba $10 million for a technology it had no use for. He compared the new information with earlier observations about the digital music market.

Then something much more interesting happened. The iPod was an instant hit, changing competition. Other computer businesses that competed in laptops, desktops, and servers created digital music players. Microsoft's Zune came out in 2006, Dell's Digital Jukebox in 2004. Both flopped.

By then, Apple was poised to unveil the iPhone, which would cause its competitors to Observe, Orient, Decide, and Act. Boyd named this OODA Loop infiltration. They couldn't gain the initiative by constantly reacting to Apple.

Microsoft and Dell were titans back then, but it's hard to recall. Apple went from near bankruptcy to crushing its competition via Schwerpunkt.

Rather than a destination, it is a journey

Trying to win everywhere is a strategic blunder. Win significant fights, not trivial skirmishes. Identifying a focal point to direct resources and efforts is the essence of Schwerpunkt.

When Steve Jobs returned to Apple, PC firms were competing, but he focused on digital music players, and the iPod made Apple a player. He launched the iPhone when his competitors were still reacting. When Steve Jobs said, "One more thing," at the end of a product presentation, he had a new focus.

Schwerpunkt isn't static; it's dynamic. Jobs' ability to observe, refocus, and modify the competitive backdrop allowed Apple to innovate consistently. His strategy was tailored to Apple's capabilities, customers, and ecosystem. Microsoft or Dell, better suited for the enterprise sector, couldn't succeed with a comparable approach.

There is no optimal strategy, only ones suited to a given environment, when relative strength might be used against relative weakness. Discovering the center of gravity where you can break through is more of a journey than a destination; it will become evident after you reach.

Ethan Siegel

Ethan Siegel

1 year ago

How you view the year will change after using this one-page calendar.

The conventional way we display annual calendars, at left, requires us to examine each month separately, either relegating the full year to a tiny font on a single page or onto 12 separate pages. Instead, the one-page calendar, at right, enables you to find whatever you want all throughout the year. (Credit: E. Siegel, with a public domain conventional calendar at left)

No other calendar is simpler, smaller, and reusable year after year. It works and is used here.

Most of us discard and replace our calendars annually. Each month, we move our calendar ahead another page, thus if we need to know which day of the week corresponds to a given day/month combination, we have to calculate it or flip forward/backward to the corresponding month. Questions like:

  • What day does this year's American Thanksgiving fall on?

  • Which months contain a Friday the thirteenth?

  • When is July 4th? What day of the week?

  • Alternatively, what day of the week is Christmas?

They're hard to figure out until you switch to the right month or look up all the months.

However, mathematically, the answers to these questions or any question that requires matching the day of the week with the day/month combination in a year are predictable, basic, and easy to work out. If you use this one-page calendar instead of a 12-month calendar, it lasts the whole year and is easy to alter for future years. Let me explain.

Rather than a calendar displaying separate images for each month out of the year, this one-page calendar can be used to match up the day of the week with the dates/months of the year with perfect accuracy all in a single view. (Credit: E. Siegel)

The 2023 one-page calendar is above. The days of the month are on the lower left, which works for all months if you know that:

  • There are 31 days in January, March, May, July, August, October, and December.

  • All of the months of April, June, September, and November have 30 days.

  • And depending on the year, February has either 28 days (in non-leap years) or 29 days (in leap years).

If you know this, this calendar makes it easy to match the day/month of the year to the weekday.

Here are some instances. American Thanksgiving is always on the fourth Thursday of November. You'll always know the month and day of the week, but the date—the day in November—changes each year.

On any other calendar, you'd have to flip to November to see when the fourth Thursday is. This one-page calendar only requires:

  • pick the month of November in the top-right corner to begin.

  • drag your finger down until Thursday appears,

  • then turn left and follow the monthly calendar until you reach the fourth Thursday.

To find American Thanksgiving, you need to find the 4th Thursday in November. Using the one-page calendar, start at November, move down to find Thursday, then move to the left to count off to the fourth Thursday in November. In 2023, that date will be November 23rd. (Credit: E. Siegel)

It's obvious: 2023 is the 23rd American Thanksgiving. For every month and day-of-the-week combination, start at the month, drag your finger down to the desired day, and then move to the left to see which dates match.

What if you knew the day of the week and the date of the month, but not the month(s)?

A different method using the same one-page calendar gives the answer. Which months have Friday the 13th this year? Just:

  • begin on the 13th of the month, the day you know you desire,

  • then swipe right with your finger till Friday appears.

  • and then work your way up until you can determine which months the specific Friday the 13th falls under.

If you know which date/day-of-the-week combination you’re seeking but don’t know which months will meet that criteria, start with the date (1–31), move to the right until you find the day of the week you want, then move up and find which months match that criteria. Every year will always have at least one such combination. (Credit: E. Siegel)

One Friday the 13th occurred in January 2023, and another will occur in October.

The most typical reason to consult a calendar is when you know the month/day combination but not the day of the week.

Compared to single-month calendars, the one-page calendar excels here. Take July 4th, for instance. Find the weekday here:

  • beginning on the left on the fourth of the month, as you are aware,

  • also begin with July, the month of the year you are most familiar with, at the upper right,

  • you should move your two fingers in the opposite directions till they meet: on a Tuesday in 2023.

That's how you find your selected day/month combination's weekday.

If you were curious as to which day of the week July 4th, 2023 fell on, rather than flipping a conventional calendar to July and seeing, you could trace “4” to the right and “July” down, finding where they meet (on a Tuesday) revealing the day-of-the-week. (Credit: E. Siegel)

Another example: Christmas. Christmas Day is always December 25th, however unless your conventional calendar is open to December of your particular year, a question like "what day of the week is Christmas?" difficult to answer.

Unlike the one-page calendar!

Remember the left-hand day of the month. Top-right, you see the month. Put two fingers, one from each hand, on the date (25th) and the month (December). Slide the day hand to the right and the month hand downwards until they touch.

They meet on Monday—December 25, 2023.

Using the one-page calendar for 2023, you can figure out the day-of-the-week of any calendar day by placing one finger on the “date” at left and another on the “month” at top. By moving your fingers respectively to the right and down, where they meet will reveal the day of the week to you. (Credit: E. Siegel)

For 2023, that's fine, but what happens in 2024? Even worse, what if we want to know the day-of-the-week/day/month combo many years from now?

I think the one-page calendar shines here.

Except for the blue months in the upper-right corner of the one-page calendar, everything is the same year after year. The months also change in a consistent fashion.

Each non-leap year has 365 days—one more than a full 52 weeks (which is 364). Since January 1, 2023 began on a Sunday and 2023 has 365 days, we immediately know that December 31, 2023 will conclude on a Sunday (which you can confirm using the one-page calendar) and that January 1, 2024 will begin on a Monday. Then, reorder the months for 2024, taking in mind that February will have 29 days in a leap year.

This image shows the one-page calendar view for the next leap year we’re going to experience: 2024. Note that the monthly patterns have changed from how they were in a non-leap year, displaying a new pattern unique to leap years, corresponding to the fact that February has 29 days instead of 28. (Credit: E. Siegel)

Please note the differences between 2023 and 2024 month placement. In 2023:

  • October and January began on the same day of the week.

  • On the following Monday of the week, May began.

  • August started on the next day,

  • then the next weekday marked the start of February, March, and November, respectively.

  • Unlike June, which starts the following weekday,

  • While September and December start on the following day of the week,

  • Lastly, April and July start one extra day later.

Since 2024 is a leap year, February has 29 days, disrupting the rhythm. Month placements change to:

  • The first day of the week in January, April, and July is the same.

  • October will begin the following day.

  • Possibly starting the next weekday,

  • February and August start on the next weekday,

  • beginning on the following day of the week between March and November,

  • beginning the following weekday in June,

  • and commencing one more day of the week after that, September and December.

Due to the 366-day leap year, 2025 will start two days later than 2024 on January 1st.

The non-leap year 2025 has the same calendar as 2023, expect with the days-of-the-week that each month begins on shifted forward by three days for each month. This is because 2023 was not a leap year and 2024 was, meaning that an extra 3 days are needed over and above the 104 full weeks contained in 2023 and 2024 combined. (Credit: E. Siegel)

Now, looking at the 2025 calendar, you can see that the 2023 pattern of which months start on which days is repeated! The sole variation is a shift of three days-of-the-week ahead because 2023 had one more day (365) than 52 full weeks (364), and 2024 had two more days (366). Again,

  • On Wednesday this time, January and October begin on the same day of the week.

  • Although May begins on Thursday,

  • August begins this Friday.

  • March, November, and February all begin on a Saturday.

  • Beginning on a Sunday in June

  • Beginning on Monday are September and December,

  • and on Tuesday, April and July begin.

In 2026 and 2027, the year will commence on a Thursday and a Friday, respectively.

The one-page calendars for 2026 and 2027, as shown next to one another. Note that the calendars are identical, save that the day-of-the-week that each month begins on is shifted by one day from the prior year to the next. This occurs every time a non-leap year is followed by another non-leap year. (Credit: E. Siegel)

We must return to our leap year monthly arrangement in 2028. Yes, January 1, 2028 begins on a Saturday, but February, which begins on a Tuesday three days before January, will have 29 days. Thus:

  • Start dates for January, April, and July are all Saturdays.

  • Given that October began on Sunday,

  • Although May starts on a Monday,

  • beginning on a Tuesday in February and August,

  • Beginning on a Wednesday in March and November,

  • Beginning on Thursday, June

  • and Friday marks the start of September and December.

This is great because there are only 14 calendar configurations: one for each of the seven non-leap years where January 1st begins on each of the seven days of the week, and one for each of the seven leap years where it begins on each day of the week.

This example of a one-page calendar, which represents the year 2028, will be valid for all leap years that begin with January 1st on a Saturday. The leap year version of the one-page calendar repeats every 28 years, unless you pass a non-leap year ending in “00,” in which case the repeat will either be 12 or 40 years instead. (Credit: E. Siegel)

The 2023 calendar will function in 2034, 2045, 2051, 2062, 2073, 2079, 2090, 2102, 2113, and 2119. Except when passing over a non-leap year that ends in 00, like 2100, the repeat time always extends to 12 years or shortens to an extra 6 years.

  • The pattern is repeated in 2025's calendar in 2031, 2042, 2053, 2059, 2070, 2081, 2087, 2098, 2110, and 2121.

  • The extra 6-year repeat at the end of the century on the calendar for 2026 will occur in the years 2037, 2043, 2054, 2065, 2071, 2082, 2093, 2099, 2105, and 2122.

  • The 2027s calendar repeats in 2038, 2049, 2055, 2066, 2077, 2083, 2094, 2100, 2106, and 2117, almost exactly matching the 2026s pattern.

For leap years, the recurrence pattern is every 28 years when not passing a non-leap year ending in 00, or 12 or 40 years when we do. 2024's calendar repeats in 2052, 2080, 2120, 2148, 2176, and 2216; 2028's in 2056, 2084, 2124, 2152, 2180, and 2220.

Knowing January 1st and whether it's a leap year lets you construct a one-page calendar for any year. Try it—you might find it easier than any other alternative!