Prioritize big-ticket purchases

I've made several spending blunders. I get sick thinking about how much money I spent.

My financial mental model was poor back then.

Stoicism and mindfulness keep me from attaching to those feelings. It still hurts.

Until four or five years ago, I bought a new winter jacket every year.

Ten years ago, I spent twice as much. Now that I have a fantastic, warm winter parka, I don't even consider acquiring another one. No more spending. I'm not looking for jackets either.

Saving time and money by spending well is my thinking paradigm.

The philosophy is expressed in most languages. Cheap is expensive in the Netherlands. This applies beyond shopping.

In this essay, I will offer three examples of how this mental paradigm transformed my financial life.

Publishing books

In 2015, I presented and positioned my first book poorly.

I called the book Huge Life Success and made a funny Canva cover in 30 minutes. This:

That looks nothing like my present books. No logo or style. The book felt amateurish.

The book started bothering me a few weeks after publication. The advice was good, but it didn't appear professional. I studied the book business extensively.

I created a style for all my designs. Branding. Win Your Inner Wars was reissued a year later.

Title, cover, and description changed. Rearranging the chapters improved readability.

Seven years later, the book sells hundreds of copies a month. That taught me a lot.

Rushing to finish a project is enticing. Send it and move forward.

Avoid rushing everything. Relax. Develop your projects. Perform well. Perform the job well.

My first novel was underfunded and underworked. A bad book arrived. I then invested time and money in writing the greatest book I could.

That book still sells.

Traveling

I hate travel. Airports, flights, trains, and lines irritate me.

But, I enjoy traveling to beautiful areas.

I do it strangely. I make up travel rules. I never go to airports in summer. I hate being near airports on holidays. Unworthy.

No vacation packages for me. Those airline packages with a flight, shuttle, and hotel. I've had enough.

I try to avoid crowds and popular spots. July Paris? Nuts and bolts, please. Christmas in NYC? No, please keep me sane.

I fly business class behind. I accept upgrades upon check-in. I prefer driving. I drove from the Netherlands to southern Spain.

Thankfully, no lines. What if travel costs more? Thus? I enjoy it from the start. I start traveling then.

I rarely travel since I'm so difficult. One great excursion beats several average ones.

Personal effectiveness

New apps, tools, and strategies intrigue most productivity professionals.

No.

I researched years ago. I spent years investigating productivity in university.

I bought books, courses, applications, and tools. It was expensive and time-consuming.

Im finished. Productivity no longer costs me time or money. OK. I worked on it once and now follow my strategy.

I avoid new programs and systems. My stuff works. Why change winners?

Spending wisely saves time and money.

Spending wisely means spending once. Many people ignore productivity. It's understudied. No classes.

Some assume reading a few articles or a book is enough. Productivity is personal. You need a personal system.

Time invested is one-time. You can trust your system for life once you find it.

Concentrate on the expensive choices.

Life's short. Saving money quickly is enticing.

Spend less on groceries today. True. That won't fix your finances.

Adopt a lifestyle that makes you affluent over time. Consider major choices.

Are they causing long-term poverty? Are you richer?

Leasing cars comes to mind. The automobile costs a fortune today. The premium could accomplish a million nice things.

Focusing on important decisions makes life easier. Consider your future. You want to improve next year.

Taking great financial advice is key to financial success.

A wealthy man told me to INVEST MY MONEY when I was young.

As I entered Starbucks, an older man was leaving. I noticed his watch and expensive-looking shirt, not like the guy in the photo, but one made of fine fabric like vicuna wool, which can only be shorn every two to three years. His Bentley confirmed my suspicions about his wealth.

This guy looked like James Bond, so I asked him how to get rich like him.

"Drug dealer?" he laughed.

Whether he was telling the truth, I'll never know, and I didn't want to be an accessory, but he quickly added, "Kid, invest your money; it will do wonders." He left.

When he told me to invest, he didn't say what. Later, I realized the investment game has so many levels that even if he drew me a blueprint, I wouldn't understand it.

The best advice I received was to invest my earnings. I must decide where to invest.

I'll preface by saying I'm not a financial advisor or Your financial advisor, but I'll share what I've learned from books, links, and sources. The rest is up to you.

Basically:

Invest your Money

Money is money, whether you call it cake, dough, moolah, benjamins, paper, bread, etc.

If you're lucky, you can buy one of the gold shirts in the photo.

Investing your money today means putting it towards anything that could be profitable.

According to the website Investopedia:
“Investing is allocating money to generate income or profit.”

You can invest in a business, real estate, or a skill that will pay off later.

Everyone has different goals and wants at different stages of life, so investing varies.

He was probably a sugar daddy with his Bentley, nice shirt, and Rolex.

In my twenties, I started making "good" money; now, in my forties, with a family and three kids, I'm building a legacy for my grandkids.

“It’s not how much money you make, but how much money you keep, how hard it works for you, and how many generations you keep it for.” — Robert Kiyosaki.

Money isn't evil, but lack of it is.

Financial stress is a major source of problems, according to studies. 

Being broke hurts, especially if you want to provide for your family or do things.

“An investment in knowledge pays the best interest.” — Benjamin Franklin.

Investing in knowledge is invaluable. Before investing, do your homework.

You probably didn't learn about investing when you were young, like I didn't. My parents were in survival mode, making investing difficult.

In my 20s, I worked in banking to better understand money.

So, why invest?

Growth requires investment.

Investing puts money to work and can build wealth. Your money may outpace inflation with smart investing. Compounding and the risk-return tradeoff boost investment growth.

Investing your money means you won't have to work forever — unless you want to.

Two common ways to make money are;

-working hard,

and

-interest or capital gains from investments.

Capital gains can help you invest.

“How many millionaires do you know who have become wealthy by investing in savings accounts? I rest my case.” — Robert G. Allen

If you keep your money in a savings account, you'll earn less than 2% interest at best; the bank makes money by loaning it out.

Savings accounts are a safe bet, but the low-interest rates limit your gains.

Don't skip it. An emergency fund should be in a savings account, not the market.

Other reasons to invest:

Investing can generate regular income.

If you own rental properties, the tenant's rent will add to your cash flow.

Daily, weekly, or monthly rentals (think Airbnb) generate higher returns year-round.

Capital gains are taxed less than earned income if you own dividend-paying or appreciating stock.

Time is on your side

“Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t — pays it.” — Albert Einstein

Historical data shows that young investors outperform older investors. So you can use compound interest over decades instead of investing at 45 and having less time to earn.

If I had taken that man's advice and invested in my twenties, I would have made a decent return by my thirties. (Depending on my investments)

So for those who live a YOLO (you only live once) life, investing can't hurt.

Investing increases your knowledge.

Lessons are clearer when you're invested. Each win boosts confidence and draws attention to losses. Losing money prompts you to investigate.

Before investing, I read many financial books, but I didn't understand them until I invested.

Now what?

What do you invest in? Equities, mutual funds, ETFs, retirement accounts, savings, business, real estate, cryptocurrencies, marijuana, insurance, etc.

The key is to start somewhere. Know you don't know everything. You must care.

“A journey of a thousand miles must begin with a single step.” — Lao Tzu.

Start simple because there's so much information. My first investment book was:

Robert Kiyosaki's "Rich Dad, Poor Dad"

This easy-to-read book made me hungry for more. This book is about the money lessons rich parents teach their children, which poor and middle-class parents neglect. The poor and middle-class work for money, while the rich let their assets work for them, says Kiyosaki.

There is so much to learn, but you gotta start somewhere.

More books:

***Wisdom

I hope I'm not suggesting that investing makes everything rosy. Remember three rules:

1. Losing money is possible.

2. Losing money is possible.

3. Losing money is possible.

You can lose money, so be careful.

Read, research, invest.

Golden rules for Investing your money

• Never invest money you can't lose.

• Financial freedom is possible regardless of income.

• "Courage taught me that any sound investment will pay off, no matter how bad a crisis gets." Helu Carlos

• "I'll tell you Wall Street's secret to wealth. When others are afraid, you're greedy. You're afraid when others are greedy. Buffett

• Buy low, sell high, and have an exit strategy.

• Ask experts or wealthy people for advice.

• "With a good understanding of history, we can have a clear vision of the future." Helu Carlos

• "It's not whether you're right or wrong, but how much money you make when you're right." Soros

• "The individual investor should act as an investor, not a speculator." Graham

• "It's different this time" is the most dangerous investment phrase. Templeton

Lastly,

• Avoid quick-money schemes. Building wealth takes years, not months.

Start small and work your way up.

Thanks for reading!

This post is a summary. Read the full article here

https://tomconnor.me/wp-content/uploads/2021/08/10x-Engineer-Mental-Models.pdf

I keep returning to the same mental models and tricks after writing and reading about a wide range of topics.

Top 12 mental models

12.

Survival bias - We perceive the surviving population as remarkable, yet they may have gotten there through sheer grit.

Survivorship bias affects us in many situations. Our retirement fund; the unicorn business; the winning team. We often study and imitate the last one standing. This can lead to genuine insights and performance improvements, but it can also lead us astray because the leader may just be lucky.

11.

The Helsinki Bus Theory - How to persevere Buss up!

Always display new work, and always be compared to others. Why? Easy. Keep riding. Stay on the fucking bus.

10.

Until it sticks… Turning up every day… — Artists teach engineers plenty. Quality work over a career comes from showing up every day and starting.

9.

WRAP decision making process (Heath Brothers)

Decision-making WRAP Model:

W — Widen your Options

R — Reality test your assumptions

A — Attain Distance

P — Prepare to be wrong or Right

8.

Systems for knowledge worker excellence - Todd Henry and Cal Newport write about techniques knowledge workers can employ to build a creative rhythm and do better work.

Todd Henry's FRESH framework:

1. Focus: Keep the start in mind as you wrap up.

2. Relationships: close a loop that's open.

3. Pruning is an energy.

4. Set aside time to be inspired by stimuli.

5. Hours: Spend time thinking.

7.

Black Box Thinking…..

BBT is learning from mistakes. Science has transformed the world because it constantly updates its theories in light of failures. Complexity guarantees failure. Do we learn or self-justify?

6.

The OODA Loop - Competitive advantage

O: Observe: collect the data. Figure out exactly where you are, what’s happening.

O: Orient: analyze/synthesize the data to form an accurate picture.

D: Decide: select an action from possible options

A: Action: execute the action, and return to step (1)

Boyd's approach indicates that speed and agility are about information processing, not physical reactions. They form feedback loops. More OODA loops improve speed.

5.

Know your Domain 

Leaders who try to impose order in a complex situation fail; those who set the stage, step back, and allow patterns to develop win.

https://vimeo.com/640941172?embedded=true&source=vimeo_logo&owner=11999906

4.

The Three Critical Gaps

• Information Gap - The discrepancy between what we know and what we would like to know

• Gap in Alignment - What individuals actually do as opposed to what we wish them to do

• Effects Gap - the discrepancy between our expectations and the results of our actions

3.

Theory of Constraints — The Goal  - To maximize system production, maximize bottleneck throughput.

• Goldratt creates a five-step procedure:

1. Determine the restriction

2. Improve the restriction.

3. Everything else should be based on the limitation.

4. Increase the restriction

5. Go back to step 1 Avoid letting inertia become a limitation.

Any non-constraint improvement is an illusion.

2.

Serendipity and the Adjacent Possible - Why do several amazing ideas emerge at once? How can you foster serendipity in your work?

You need specialized abilities to reach to the edge of possibilities, where you can pursue exciting tasks that will change the world. Few people do it since it takes a lot of hard work. You'll stand out if you do.

Most people simply lack the comfort with discomfort required to tackle really hard things. At some point, in other words, there’s no way getting around the necessity to clear your calendar, shut down your phone, and spend several hard days trying to make sense of the damn proof.

1.

Boundaries of failure - Rasmussen's accident model.

Rasmussen modeled this. It has economic, workload, and performance boundaries.

The economic boundary is a company's profit zone. If the lights are on, you're within the economic boundaries, but there's pressure to cut costs and do more.

Performance limit reflects system capacity. Taking shortcuts is a human desire to minimize work. This is often necessary to survive because there's always more labor.

Both push operating points toward acceptable performance. Personal or process safety, or equipment performance.

If you exceed acceptable performance, you'll push back, typically forcefully.

DATA MINING WITH SUPERALGORES

Old pots produce the best soup.

Science has always inspired indicator design. From physics to signal processing, many indicators use concepts from mechanical engineering, electronics, and probability. In Superalgos' Data Mining section, we've explored using thermodynamics and information theory to construct indicators and using statistical and probabilistic techniques like reduced normal law to take advantage of low probability events.

An asset's price is like a mechanical object revolving around its moving average. Using this approach, we could design an indicator using the oscillator's Total Energy. An oscillator's energy is finite and constant. Since we don't expect the price to follow the harmonic oscillator, this energy should deviate from the perfect situation, and the maximum of divergence may provide us valuable information on the price's moving average.

Definition of the Harmonic Oscillator in Few Words

Sinusoidal function describes a harmonic oscillator. The time-constant energy equation for a harmonic oscillator is:

With

Time saves energy.

In a mechanical harmonic oscillator, total energy equals kinetic energy plus potential energy. The formula for energy is the same for every kind of harmonic oscillator; only the terms of total energy must be adapted to fit the relevant units. Each oscillator has a velocity component (kinetic energy) and a position to equilibrium component (potential energy).

The Price Oscillator and the Energy Formula

Considering the harmonic oscillator definition, we must specify kinetic and potential components for our price oscillator. We define oscillator velocity as the rate of change and equilibrium position as the price's distance from its moving average.

Price kinetic energy:

It's like:

With

and

L is the number of periods for the rate of change calculation and P for the close price EMA calculation.

Total price oscillator energy =

Given that an asset's price can theoretically vary at a limitless speed and be endlessly far from its moving average, we don't expect this formula's outcome to be constrained. We'll normalize it using Z-Score for convenience of usage and readability, which also allows probabilistic interpretation.

Over 20 periods, we'll calculate E's moving average and standard deviation.

We calculated Z on BTC/USDT with L = 10 and P = 21 using Knime Analytics.

The graph is detrended. We added two horizontal lines at +/- 1.6 to construct a 94.5% probability zone based on reduced normal law tables. Price cycles to its moving average oscillate clearly. Red and green arrows illustrate where the oscillator crosses the top and lower limits, corresponding to the maximum/minimum price oscillation. Since the results seem noisy, we may apply a non-lagging low-pass or multipole filter like Butterworth or Laguerre filters and employ dynamic bands at a multiple of Z's standard deviation instead of fixed levels.

Kinetic Detrender Implementation in Superalgos

The Superalgos Kinetic detrender features fixed upper and lower levels and dynamic volatility bands.

The code is pretty basic and does not require a huge amount of code lines.

It starts with the standard definitions of the candle pointer and the constant declaration :

let candle = record.current
let len = 10
let P = 21
let T = 20
let up = 1.6
let low = 1.6

Upper and lower dynamic volatility band constants are up and low.

We proceed to the initialization of the previous value for EMA :

if (variable.prevEMA === undefined) {
    variable.prevEMA = candle.close
}

And the calculation of EMA with a function (it is worth noticing the function is declared at the end of the code snippet in Superalgos) :

variable.ema = calculateEMA(P, candle.close, variable.prevEMA)
//EMA calculation
function calculateEMA(periods, price, previousEMA) {
    let k = 2 / (periods + 1)
    return price * k + previousEMA * (1 - k)
}

The rate of change is calculated by first storing the right amount of close price values and proceeding to the calculation by dividing the current close price by the first member of the close price array:

variable.allClose.push(candle.close)
if (variable.allClose.length > len) {
    variable.allClose.splice(0, 1)
}
if (variable.allClose.length === len) {
    variable.roc = candle.close / variable.allClose[0]
} else {
    variable.roc = 1
}

Finally, we get energy with a single line:

variable.E = 1 / 2 * len * variable.roc + 1 / 2 * P * candle.close / variable.ema

The Z calculation reuses code from Z-Normalization-based indicators:

variable.allE.push(variable.E)
if (variable.allE.length > T) {
    variable.allE.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allE.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allE[i]
    }
    variable.MA = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allE[i] - variable.MA, 2)
    }
    variable.sigma = Math.sqrt(variable.SQ / T)
variable.Z = (variable.E - variable.MA) / variable.sigma
} else {
    variable.Z = 0
}
variable.allZ.push(variable.Z)
if (variable.allZ.length > T) {
    variable.allZ.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allZ.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allZ[i]
    }
    variable.MAZ = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allZ[i] - variable.MAZ, 2)
    }
    variable.sigZ = Math.sqrt(variable.SQ / T)
} else {
    variable.MAZ = variable.Z
    variable.sigZ = variable.MAZ * 0.02
}
variable.upper = variable.MAZ + up * variable.sigZ
variable.lower = variable.MAZ - low * variable.sigZ

We also update the EMA value.

variable.prevEMA = variable.EMA

Conclusion

We showed how to build a detrended oscillator using simple harmonic oscillator theory. Kinetic detrender's main line oscillates between 2 fixed levels framing 95% of the values and 2 dynamic levels, leading to auto-adaptive mean reversion zones.

Superalgos' Normalized Momentum data mine has the Kinetic detrender indication.

All the material here can be reused and integrated freely by linking to this article and Superalgos.

This post is informative and not financial advice. Seek expert counsel before trading. Risk using this material.

One great idea might make you rich.

Imagine having a million-dollar concept in college that made a million.

2005 precisely.

Alex Tew, 21, from Wiltshire, England, created The Million Dollar Homepage in August 2005. The idea is basic but beyond the ordinary, which is why it worked.

Alex built a 1,000,000-pixel webpage.

Each website pixel would cost $1. Since pixels are hard to discern, he sold 10x10 squares for $100.

He'd make a million if all the spots sold.

He may have thought about NFTs and the Metaverse decades ago.

MillionDollarHomepage.com launched in 2005.

Businesses and individuals could buy a website spot and add their logo, website link, and tagline. You bought an ad, but nobody visited the website.

If a few thousand people visited the website, it could drive traffic to your business's site.

Alex promised buyers the website would be up for 5 years, so it was a safe bet.

Alex's friend with a music website was the first to buy real estate on the site. Within two weeks, 4,700 pixels sold, and a tracker showed how many were sold and available.

Word-of-mouth marketing got the press's attention quickly. Everyone loves reading about new ways to make money, so it was a good news story.

By September, over 250,000 pixels had been sold, according to a BBC press release.

Alex and the website gained more media and public attention, so traffic skyrocketed. Two months after the site launched, 1,400 customers bought more than 500,000 pixels.

Businesses bought online real estate. They heard thousands visited the site, so they could get attention cheaply.

Unless you bought a few squares, I'm not sure how many people would notice your ad or click your link.

A sponge website owner emailed Alex:

“We tried Million Dollar Homepage because we were impressed at the level of ingenuity and the sheer simplicity of it. If we’re honest, we didn’t expect too much from it. Now, as a direct result, we are pitching for £18,000 GBP worth of new clients and have seen our site traffic increase over a hundred-fold. We’re even going to have to upgrade our hosting facility! It’s been exceptional.”

Web.archive.org screenshots show how the website changed.

“The idea is to create something of an internet time capsule: a homepage that is unique and permanent. Everything on the internet keeps changing so fast, it will be nice to have something that stays solid and permanent for many years. You can be a part of that!” Alex Tew, 2005

The last 1,000 pixels were sold on January 1, 2006.

By then, the homepage had hundreds of thousands of monthly visitors. Alex put the last space on eBay due to high demand.

MillionDollarWeightLoss.com won the last pixels for $38,100, bringing revenue to $1,037,100 in 4 months.

Many have tried to replicate this website's success. They've all failed.

This idea only worked because no one had seen this website before.

This winner won't be repeated, but it should inspire you to try something new and creative.

Still popular, you could buy one of the linked domains. You can't buy pixels, but you can buy an expired domain.

One link I clicked costs $59,888.

You'd own a piece of internet history if you spent that much on a domain.

Someone bought stablesgallery.co.uk after the domain expired and restored it.

Many of the linked websites have expired or been redirected, but some still link to the original. I couldn't find sponge's website. Can you?

This is a great example of how a simple creative idea can go viral.

Comment on this amazing success story.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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!