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Katrina Paulson

Katrina Paulson

3 years ago

Dehumanization Against Anthropomorphization

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Bob Service

Bob Service

3 years ago

Did volcanic 'glasses' play a role in igniting early life?

Quenched lava may have aided in the formation of long RNA strands required by primitive life.

It took a long time for life to emerge. Microbes were present 3.7 billion years ago, just a few hundred million years after the 4.5-billion-year-old Earth had cooled enough to sustain biochemistry, according to fossils, and many scientists believe RNA was the genetic material for these first species. RNA, while not as complicated as DNA, would be difficult to forge into the lengthy strands required to transmit genetic information, raising the question of how it may have originated spontaneously.

Researchers may now have a solution. They demonstrate how basaltic glasses assist individual RNA letters, also known as nucleoside triphosphates, join into strands up to 200 letters long in lab studies. The glasses are formed when lava is quenched in air or water, or when melted rock generated by asteroid strikes cools rapidly, and they would have been plentiful in the early Earth's fire and brimstone.

The outcome has caused a schism among top origin-of-life scholars. "This appears to be a great story that finally explains how nucleoside triphosphates react with each other to create RNA strands," says Thomas Carell, a scientist at Munich's Ludwig Maximilians University. However, Harvard University's Jack Szostak, an RNA expert, says he won't believe the results until the study team thoroughly describes the RNA strands.

Researchers interested in the origins of life like the idea of a primordial "RNA universe" since the molecule can perform two different functions that are essential for life. It's made up of four chemical letters, just like DNA, and can carry genetic information. RNA, like proteins, can catalyze chemical reactions that are necessary for life.

However, RNA can cause headaches. No one has yet discovered a set of plausible primordial conditions that would cause hundreds of RNA letters—each of which is a complicated molecule—to join together into strands long enough to support the intricate chemistry required to kick-start evolution.

Basaltic glasses may have played a role, according to Stephen Mojzsis, a geologist at the University of Colorado, Boulder. They're high in metals like magnesium and iron, which help to trigger a variety of chemical reactions. "Basaltic glass was omnipresent on Earth at the time," he adds.

He provided the Foundation for Applied Molecular Evolution samples of five different basalt glasses. Each sample was ground into a fine powder, sanitized, and combined with a solution of nucleoside triphosphates by molecular biologist Elisa Biondi and her colleagues. The RNA letters were unable to link up without the presence of glass powder. However, when the molecules were mixed with the glass particles, they formed long strands of hundreds of letters, according to the researchers, who published their findings in Astrobiology this week. There was no need for heat or light. Biondi explains, "All we had to do was wait." After only a day, little RNA strands produced, yet the strands continued to grow for months. Jan Paek, a molecular biologist at Firebird Biomolecular Sciences, says, "The beauty of this approach is its simplicity." "Mix the components together, wait a few days, and look for RNA."

Nonetheless, the findings pose a slew of problems. One of the questions is how nucleoside triphosphates came to be in the first place. Recent study by Biondi's colleague Steven Benner suggests that the same basaltic glasses may have aided in the creation and stabilization of individual RNA letters.

The form of the lengthy RNA strands, according to Szostak, is a significant challenge. Enzymes in modern cells ensure that most RNAs form long linear chains. RNA letters, on the other hand, can bind in complicated branching sequences. Szostak wants the researchers to reveal what kind of RNA was produced by the basaltic glasses. "It irritates me that the authors made an intriguing initial finding but then chose to follow the hype rather than the research," Szostak says.

Biondi acknowledges that her team's experiment almost probably results in some RNA branching. She does acknowledge, however, that some branched RNAs are seen in species today, and that analogous structures may have existed before the origin of life. Other studies carried out by the study also confirmed the presence of lengthy strands with connections, indicating that they are most likely linear. "It's a healthy argument," says Dieter Braun, a Ludwig Maximilian University origin-of-life chemist. "It will set off the next series of tests."

Michael Hunter, MD

Michael Hunter, MD

3 years ago

5 Drugs That May Increase Your Risk of Dementia

Photo by danilo.alvesd on Unsplash

While our genes can't be changed easily, you can avoid some dementia risk factors. Today we discuss dementia and five drugs that may increase risk.

Memory loss appears to come with age, but we're not talking about forgetfulness. Sometimes losing your car keys isn't an indication of dementia. Dementia impairs the capacity to think, remember, or make judgments. Dementia hinders daily tasks.

Alzheimers is the most common dementia. Dementia is not normal aging, unlike forgetfulness. Aging increases the risk of Alzheimer's and other dementias. A family history of the illness increases your risk, according to the Mayo Clinic (USA).

Given that our genes are difficult to change (I won't get into epigenetics), what are some avoidable dementia risk factors? Certain drugs may cause cognitive deterioration.

Today we look at four drugs that may cause cognitive decline.

Dementia and benzodiazepines

Benzodiazepine sedatives increase brain GABA levels. Example benzodiazepines:

  • Diazepam (Valium) (Valium)

  • Alprazolam (Xanax) (Xanax)

  • Clonazepam (Klonopin) (Klonopin)

Addiction and overdose are benzodiazepine risks. Yes! These medications don't raise dementia risk.

USC study: Benzodiazepines don't increase dementia risk in older adults.

Benzodiazepines can produce short- and long-term amnesia. This memory loss hinders memory formation. Extreme cases can permanently impair learning and memory. Anterograde amnesia is uncommon.

2. Statins and dementia

Statins reduce cholesterol. They prevent a cholesterol-making chemical. Examples:

  • Atorvastatin (Lipitor) (Lipitor)

  • Fluvastatin (Lescol XL) (Lescol XL)

  • Lovastatin (Altoprev) (Altoprev)

  • Pitavastatin (Livalo, Zypitamag) (Livalo, Zypitamag)

  • Pravastatin (Pravachol) (Pravachol)

  • Rosuvastatin (Crestor, Ezallor) (Crestor, Ezallor)

  • Simvastatin (Zocor) (Zocor)

Photo by Towfiqu barbhuiya on Unsplash

This finding is contentious. Harvard's Brigham and Womens Hospital's Dr. Joann Manson says:

“I think that the relationship between statins and cognitive function remains controversial. There’s still not a clear conclusion whether they help to prevent dementia or Alzheimer’s disease, have neutral effects, or increase risk.”

This one's off the dementia list.

3. Dementia and anticholinergic drugs

Anticholinergic drugs treat many conditions, including urine incontinence. Drugs inhibit acetylcholine (a brain chemical that helps send messages between cells). Acetylcholine blockers cause drowsiness, disorientation, and memory loss.

First-generation antihistamines, tricyclic antidepressants, and overactive bladder antimuscarinics are common anticholinergics among the elderly.

Anticholinergic drugs may cause dementia. One study found that taking anticholinergics for three years or more increased the risk of dementia by 1.54 times compared to three months or less. After stopping the medicine, the danger may continue.

4. Drugs for Parkinson's disease and dementia

Cleveland Clinic (USA) on Parkinson's:

Parkinson's disease causes age-related brain degeneration. It causes delayed movements, tremors, and balance issues. Some are inherited, but most are unknown. There are various treatment options, but no cure.

Parkinson's medications can cause memory loss, confusion, delusions, and obsessive behaviors. The drug's effects on dopamine cause these issues.

A 2019 JAMA Internal Medicine study found powerful anticholinergic medications enhance dementia risk.

Those who took anticholinergics had a 1.5 times higher chance of dementia. Individuals taking antidepressants, antipsychotic drugs, anti-Parkinson’s drugs, overactive bladder drugs, and anti-epileptic drugs had the greatest risk of dementia.

Anticholinergic medicines can lessen Parkinson's-related tremors, but they slow cognitive ability. Anticholinergics can cause disorientation and hallucinations in those over 70.

Photo by Wengang Zhai on Unsplash

5. Antiepileptic drugs and dementia

The risk of dementia from anti-seizure drugs varies with drugs. Levetiracetam (Keppra) improves Alzheimer's cognition.

One study linked different anti-seizure medications to dementia. Anti-epileptic medicines increased the risk of Alzheimer's disease by 1.15 times in the Finnish sample and 1.3 times in the German population. Depakote, Topamax are drugs.

Will Lockett

Will Lockett

3 years ago

Thanks to a recent development, solar energy may prove to be the best energy source.

Photo by Zbynek Burival on Unsplash

Perovskite solar cells will revolutionize everything.

Humanity is in a climatic Armageddon. Our widespread ecological crimes of the previous century are catching up with us, and planet-scale karma threatens everyone. We must adjust to new technologies and lifestyles to avoid this fate. Even solar power, a renewable energy source, has climate problems. A recent discovery could boost solar power's eco-friendliness and affordability. Perovskite solar cells are amazing.

Perovskite is a silicon-like semiconductor. Semiconductors are used to make computer chips, LEDs, camera sensors, and solar cells. Silicon makes sturdy and long-lasting solar cells, thus it's used in most modern solar panels.

Perovskite solar cells are far better. First, they're easy to make at room temperature, unlike silicon cells, which require long, intricate baking processes. This makes perovskite cells cheaper to make and reduces their carbon footprint. Perovskite cells are efficient. Most silicon panel solar farms are 18% efficient, meaning 18% of solar radiation energy is transformed into electricity. Perovskite cells are 25% efficient, making them 38% more efficient than silicon.

However, perovskite cells are nowhere near as durable. A normal silicon panel will lose efficiency after 20 years. The first perovskite cells were ineffective since they lasted barely minutes.

Recent research from Princeton shows that perovskite cells can endure 30 years. The cells kept their efficiency, therefore no sacrifices were made.

No electrical or chemical engineer here, thus I can't explain how they did it. But strangely, the team said longevity isn't the big deal. In the next years, perovskite panels will become longer-lasting. How do you test a panel if you only have a month or two? This breakthrough technique needs a uniform method to estimate perovskite life expectancy fast. The study's key milestone was establishing a standard procedure.

Lab-based advanced aging tests are their solution. Perovskite cells decay faster at higher temperatures, so scientists can extrapolate from that. The test heated the panel to 110 degrees and waited for its output to reduce by 20%. Their panel lasted 2,100 hours (87.5 days) before a 20% decline.

They did some math to extrapolate this data and figure out how long the panel would have lasted in different climates, and were shocked to find it would last 30 years in Princeton. This made perovskite panels as durable as silicon panels. This panel could theoretically be sold today.

This technology will soon allow these brilliant panels to be released into the wild. This technology could be commercially viable in ten, maybe five years.

Solar power will be the best once it does. Solar power is cheap and low-carbon. Perovskite is the cheapest renewable energy source if we switch to it. Solar panel manufacturing's carbon footprint will also drop.

Perovskites' impact goes beyond cost and carbon. Silicon panels require harmful mining and contain toxic elements (cadmium). Perovskite panels don't require intense mining or horrible materials, making their production and expiration more eco-friendly.

Solar power destroys habitat. Massive solar farms could reduce biodiversity and disrupt local ecology by destroying vital habitats. Perovskite cells are more efficient, so they can shrink a solar farm while maintaining energy output. This reduces land requirements, making perovskite solar power cheaper, and could reduce solar's environmental impact.

Perovskite solar power is scalable and environmentally friendly. Princeton scientists will speed up the development and rollout of this energy.

Why bother with fusion, fast reactors, SMRs, or traditional nuclear power? We're close to developing a nearly perfect environmentally friendly power source, and we have the tools and systems to do so quickly. It's also affordable, so we can adopt it quickly and let the developing world use it to grow. Even I struggle to justify spending billions on fusion when a great, cheap technology outperforms it. Perovskite's eco-credentials and cost advantages could save the world and power humanity's future.

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Katharine Valentino

Katharine Valentino

3 years ago

A Gun-toting Teacher Is Like a Cook With Rat Poison

Pink or blue AR-15s?

A teacher teaches; a gun kills. Killing isn't teaching. Killing is opposite of teaching.

Without 27 school shootings this year, we wouldn't be talking about arming teachers. Gun makers, distributors, and the NRA cause most school shootings. Gun makers, distributors, and the NRA wouldn't be huge business if weapons weren't profitable.

Guns, ammo, body armor, holsters, concealed carriers, bore sights, cleaner kits, spare magazines and speed loaders, gun safes, and ear protection are sold. And more guns.

And lots more profit.

Guns aren't bread. You eat a loaf of bread in a week or so and then must buy more. Bread makers will make money. Winchester 94.30–30 1899 Lever Action Rifle from 1894 still kills. (For safety, I won't link to the ad.) Gun makers don't object if you collect antique weapons, but they need you to buy the latest, in-style killing machine. The youngster who killed 19 students and 2 teachers at Robb Elementary School in Uvalde, Texas, used an AR-15. Better yet, two.

Salvador Ramos, the Robb Elementary shooter, is a "killing influencer" He pushes consumers to buy items, which benefits manufacturers and distributors. Like every previous AR-15 influencer, he profits Colt, the rifle's manufacturer, and 52,779 gun dealers in the U.S. Ramos and other AR-15 influences make us fear for our safety and our children's. Fearing for our safety, we acquire 20 million firearms a year and live in a gun culture.

So now at school, we want to arm teachers.

Consider. Which of your teachers would you have preferred in body armor with a gun drawn?

Miss Summers? Remember her bringing daisies from her yard to second grade? She handed each student a beautiful flower. Miss Summers loved everyone, even those with AR-15s. She can't shoot.

Frasier? Mr. Frasier turned a youngster over down to explain "invert." Mr. Frasier's hands shook when he wasn't flipping fifth-graders and fractions. He may have shot wrong.

Mrs. Barkley barked in high school English class when anyone started an essay with "But." Mrs. Barkley dubbed Abie a "Jewboy" and gave him terrible grades. Arming Miss Barkley is like poisoning the chef.

Think back. Do you remember a teacher with a gun? No. Arming teachers so the gun industry can make more money is the craziest idea ever.

Or maybe you agree with Ted Cruz, the gun lobby-bought senator, that more guns reduce gun violence. After the next school shooting, you'll undoubtedly talk about arming teachers and pupils. Colt will likely develop a backpack-sized, lighter version of its popular killing machine in pink and blue for kids and boys. The MAR-15? (M for mini).


This post is a summary. Read the full one here.

mbvissers.eth

mbvissers.eth

3 years ago

Why does every smart contract seem to implement ERC165?

Photo by Cytonn Photography on Unsplash

ERC165 (or EIP-165) is a standard utilized by various open-source smart contracts like Open Zeppelin or Aavegotchi.

What's it? You must implement? Why do we need it? I'll describe the standard and answer any queries.

What is ERC165

ERC165 detects and publishes smart contract interfaces. Meaning? It standardizes how interfaces are recognized, how to detect if they implement ERC165, and how a contract publishes the interfaces it implements. How does it work?

Why use ERC165? Sometimes it's useful to know which interfaces a contract implements, and which version.

Identifying interfaces

An interface function's selector. This verifies an ABI function. XORing all function selectors defines an interface in this standard. The following code demonstrates.

// SPDX-License-Identifier: UNLICENCED
pragma solidity >=0.8.0 <0.9.0;

interface Solidity101 {
    function hello() external pure;
    function world(int) external pure;
}

contract Selector {
    function calculateSelector() public pure returns (bytes4) {
        Solidity101 i;
        return i.hello.selector ^ i.world.selector;
        // Returns 0xc6be8b58
    }

    function getHelloSelector() public pure returns (bytes4) {
        Solidity101 i;
        return i.hello.selector;
        // Returns 0x19ff1d21
    }

    function getWorldSelector() public pure returns (bytes4) {
        Solidity101 i;
        return i.world.selector;
        // Returns 0xdf419679
    }
}

This code isn't necessary to understand function selectors and how an interface's selector can be determined from the functions it implements.

Run that sample in Remix to see how interface function modifications affect contract function output.

Contracts publish their implemented interfaces.

We can identify interfaces. Now we must disclose the interfaces we're implementing. First, import IERC165 like so.

pragma solidity ^0.4.20;

interface ERC165 {
    /// @notice Query if a contract implements an interface
    /// @param interfaceID The interface identifier, as specified in ERC-165
    /// @dev Interface identification is specified in ERC-165. 
    /// @return `true` if the contract implements `interfaceID` and
    ///  `interfaceID` is not 0xffffffff, `false` otherwise
    function supportsInterface(bytes4 interfaceID) external view returns (bool);
}

We still need to build this interface in our smart contract. ERC721 from OpenZeppelin is a good example.

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC721/ERC721.sol)

pragma solidity ^0.8.0;

import "./IERC721.sol";
import "./extensions/IERC721Metadata.sol";
import "../../utils/introspection/ERC165.sol";
// ...

contract ERC721 is Context, ERC165, IERC721, IERC721Metadata {
  // ...

  function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
    return
      interfaceId == type(IERC721).interfaceId ||
      interfaceId == type(IERC721Metadata).interfaceId ||
      super.supportsInterface(interfaceId);
  }
  
  // ...
}

I deleted unnecessary code. The smart contract imports ERC165, IERC721 and IERC721Metadata. The is keyword at smart contract declaration implements all three.

Kind (interface).

Note that type(interface).interfaceId returns the same as the interface selector.

We override supportsInterface in the smart contract to return a boolean that checks if interfaceId is the same as one of the implemented contracts.

Super.supportsInterface() calls ERC165 code. Checks if interfaceId is IERC165.

function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
    return interfaceId == type(IERC165).interfaceId;
}

So, if we run supportsInterface with an interfaceId, our contract function returns true if it's implemented and false otherwise. True for IERC721, IERC721Metadata, andIERC165.

Conclusion

I hope this post has helped you understand and use ERC165 and why it's employed.

Have a great day, thanks for reading!

Ethan Siegel

Ethan Siegel

2 years 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!