For some people, the glass is half empty. For others, it’s half full. And for some, the question is, How do I get this glass totally full again?

Problem-solvers are the last group. They're neutral. Pragmatists.

Problems surround them. They fix things instead of judging them. Problem-solvers improve the world wherever they go.

Some fail. Sometimes their good intentions have terrible results. Like when they try to help a grandma cross the road because she can't do it alone but discover she never wanted to.

Most programmers, software engineers, and data scientists solve problems. They use computer code to fix problems they see.

Coding is best done by understanding and solving the problem.

Despite your best intentions, building the wrong solution may have negative consequences. Helping an unwilling grandma cross the road.

How can you improve problem-solving?

1. Examine your presumptions.

Don’t think There’s a grandma, and she’s unable to cross the road. Therefore I must help her over the road. Instead think This grandma looks unable to cross the road. Let’s ask her whether she needs my help to cross it.

Maybe the grandma can’t cross the road alone, but maybe she can. You can’t tell for sure just by looking at her. It’s better to ask.

Maybe the grandma wants to cross the road. But maybe she doesn’t. It’s better to ask!

Building software is similar. Do only I find this website ugly? Who can I consult?

We all have biases, mental shortcuts, and worldviews. They simplify life.

Problem-solving requires questioning all assumptions. They might be wrong!

Think less. Ask more.

Secondly, fully comprehend the issue.

Grandma wants to cross the road? Does she want flowers from the shop across the street?

Understanding the problem advances us two steps. Instead of just watching people and their challenges, try to read their intentions.

Don't ask, How can I help grandma cross the road? Why would this grandma cross the road? What's her goal?

Understand what people want before proposing solutions.

3. Request more information. This is not a scam!

People think great problem solvers solve problems immediately. False!

Problem-solvers study problems. Understanding the problem makes solving it easy.

When you see a grandma struggling to cross the road, you want to grab her elbow and pull her over. However, a good problem solver would ask grandma what she wants. So:

Problem solver: Excuse me, ma’am? Do you wish to get over the road? Grandma: Yes indeed, young man! Thanks for asking. Problem solver: What do you want to do on the other side? Grandma: I want to buy a bouquet of flowers for my dear husband. He loves flowers! I wish the shop wasn’t across this busy road… Problem solver: Which flowers does your husband like best? Grandma: He loves red dahlia. I usually buy about 20 of them. They look so pretty in his vase at the window! Problem solver: I can get those dahlia for you quickly. Go sit on the bench over here while you’re waiting; I’ll be back in five minutes. Grandma: You would do that for me? What a generous young man you are!

A mediocre problem solver would have helped the grandma cross the road, but he might have forgotten that she needs to cross again. She must watch out for cars and protect her flowers on the way back.

A good problem solver realizes that grandma's husband wants 20 red dahlias and completes the task.

4- Rapid and intense brainstorming

Understanding a problem makes solutions easy. However, you may not have all the information needed to solve the problem.

Additionally, retrieving crucial information can be difficult.

You could start a blog. You don't know your readers' interests. You can't ask readers because you don't know who they are.

Brainstorming works here. Set a stopwatch (most smartphones have one) to ring after five minutes. In the remaining time, write down as many topics as possible.

No answer is wrong. Note everything.

Sort these topics later. Programming or data science? What might readers scroll past—are these your socks this morning?

Rank your ideas intuitively and logically. Write Medium stories using the top 35 ideas.

5 - Google it.

Doctor Google may answer this seemingly insignificant question. If you understand your problem, try googling or binging.

Someone has probably had your problem before. The problem-solver may have posted their solution online.

Use others' experiences. If you're social, ask a friend or coworker for help.

6 - Consider it later

Rest your brain.

Reread. Your brain needs rest to function.

Hustle culture encourages working 24/7. It doesn't take a neuroscientist to see that this is mental torture.

Leave an unsolvable problem. Visit friends, take a hot shower, or do whatever you enjoy outside of problem-solving.

Nap.

I get my best ideas in the morning after working on a problem. I couldn't have had these ideas last night.

Sleeping subconsciously. Leave it alone and you may be surprised by the genius it produces.

7 - Learn to live with frustration

There are problems that you’ll never solve.

Mathematicians are world-class problem-solvers. The brightest minds in history have failed to solve many mathematical problems.

A Gordian knot problem can frustrate you. You're smart!

Frustration-haters don't solve problems well. They choose simple problems to avoid frustration.

No. Great problem solvers want to solve a problem but know when to give up.

Frustration initially hurts. You adapt.

Famous last words

If you read this article, you probably solve problems. We've covered many ways to improve, so here's a summary:

1. Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?

2. Recognize the issue completely. On the surface, a problem may seem straightforward, but what's really going on? Try to see what the current situation might be building up to by thinking two steps ahead of the current situation.

3. Request more information. You are no longer a high school student. A two-sentence problem statement is not sufficient to provide a solution. Ask away if you need more details!

4. Think quickly and thoroughly. In a constrained amount of time, try to write down all your thoughts. All concepts are worthwhile! Later, you can order them.

5. Google it. There is a purpose for the internet. Use it.

6. Consider it later at night. A rested mind is more creative. It might seem counterintuitive to leave a problem unresolved. But while you're sleeping, your subconscious will handle the laborious tasks.

7. Accept annoyance as a normal part of life. Don't give up if you're feeling frustrated. It's a step in the procedure. It's also perfectly acceptable to give up on a problem because there are other, more pressing issues that need to be addressed.

You might feel stupid sometimes, but that just shows that you’re human. You care about the world and you want to make it better.

At the end of the day, that’s all there is to problem solving — making the world a little bit better.

Calmness is a vital life skill.

It aids communication. It boosts creativity and performance.

I've studied calm people's habits for years. Commonalities:

Have learned to laugh at themselves.

Those who have something to protect can’t help but make it a very serious business, which drains the energy out of the room.

They are fixated on positive pursuits like making cool things, building a strong physique, and having fun with others rather than on depressing influences like the news and gossip.

Every day, spend at least 20 minutes moving, whether it's walking, yoga, or lifting weights.

Discover ways to take pleasure in life's challenges.

Since perspective is malleable, they change their view.

Set your own needs first.

Stressed people neglect themselves and wonder why they struggle.

Prioritize self-care.

Don't ruin your life to please others.

Make something.

Calm people create more than react.

They love creating beautiful things—paintings, children, relationships, and projects.

Hold your breath, please.

If you're stressed or angry, you may be surprised how much time you spend holding your breath and tightening your belly.

Release, breathe, and relax to find calm.

Stopped rushing.

Rushing is disadvantageous.

Calm people handle life better.

Are attuned to their personal dietary needs.

They avoid junk food and eat foods that keep them healthy, happy, and calm.

Don’t take anything personally.

Stressed people control everything.

Self-conscious.

Calm people put others and their work first.

Keep their surroundings neat.

Maintaining an uplifting and clutter-free environment daily calms the mind.

Minimise negative people.

Calm people are ruthless with their boundaries and avoid negative and drama-prone people.

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.

And why we must keep arming Ukraine

Russian expatriates write about horrific news from home.

Read this from Nadin Brzezinski. She's not a native English speaker, so there are grammar errors, but her tale smells true.

Terrible truth.

There's much more that reveals Russia's grim reality.

Non-leadership. Millions of missing supplies are presumably sold for profit, leaving untrained troops without food or gear. Missile attacks pause because they run out. Fake schemes to hold talks as a way of stalling while they scramble for solutions.

Street men were mobilized. Millions will be ground up to please a crazed despot. Fear, wrath, and hunger pull apart civilization.

It's the most dystopian story, but Ukraine is worse. Destruction of a society, country, and civilization. Only the invaders' corruption and incompetence save the Ukrainians.

Rochester, NY. My suburb had many Soviet-era Ukrainian refugees. Their kids were my classmates. Fifty years later, many are still my friends. I loved their food and culture. My town has 20,000 Ukrainians.

Grieving but determined. They don't quit. They won't quit. Russians are eternal enemies.

It's the Russian people's willingness to tolerate corruption, abuse, and stupidity by their leaders. They are paying. 65000 dead. Ruined economy. No freedom to speak. Americans do not appreciate that freedom as we should.

It lets me write/publish.

Russian friends are shocked. Many are here because their parents escaped Russian anti-semitism and authoritarian oppression. A Russian cultural legacy says a strongman's methods are admirable.

A legacy of a slavery history disguised as serfdom. Peasants and Princes.

Read Tolstoy. Then Anna Karenina. The main characters are princes and counts, whose leaders are incompetent idiots with wealth and power.

Peasants who die in their wars due to incompetence are nameless ciphers.

Sound familiar?

I've spent the last 10 years of my career mastering time management. I've tried different approaches and followed multiple people and sources. My knowledge is summarized.

Great people, including entrepreneurs, master time management. I learned time management in college. I was studying Computer Science and Finance and leading Tanzanian students in Bangalore, India. I had 24 hours per day to do this and enjoy campus. I graduated and received several awards. I've learned to maximize my time. These tips and tools help me finish quickly.

Eisenhower-Box

I don't remember when I read the article. James Clear, one of my favorite bloggers, introduced me to the Eisenhower Box, which I've used for years. Eliminate waste to master time management. By grouping your activities by importance and urgency, the tool helps you prioritize what matters and drop what doesn't. If it's urgent, do it. Delegate if it's urgent but not necessary. If it's important but not urgent, reschedule it; otherwise, drop it. I integrated the tool with Trello to manage my daily tasks. Since 2007, I've done this.

James Clear's article mentions Eisenhower Box.

Essentialism rules

Greg McKeown's book Essentialism introduced me to disciplined pursuit of less. I once wrote about this. I wasn't sure what my career's real opportunities and distractions were. A non-essentialist thinks everything is essential; you want to be everything to everyone, and your life lacks satisfaction. Poor time management starts it all. Reading and applying this book will change your life.

Essential vs non-essential

Life Calendar

Most of us make corporate calendars. Peter Njonjo, founder of Twiga Foods, said he manages time by putting life activities in his core calendars. It includes family retreats, weddings, and other events. He joked that his wife always complained to him to avoid becoming a calendar item. It's key. "Time Masters" manages life's four burners, not just work and corporate life. There's no "work-life balance"; it's life.

Health, Family, Work, and Friends.

The Brutal No

In a culture where people want to look good, saying "NO" to a favor request seems rude. In reality, the crime is breaking a promise. "Time Masters" have mastered "NO".  More "YES" means less time, and more "NO" means more time for tasks and priorities. Brutal No doesn't mean being mean to your coworkers; it means explaining kindly and professionally that you have other priorities.

To-Do vs. MITs

Most people are productive with a routine to-do list. You can't be effective by just checking boxes on a To-do list. When was the last time you completed all of your daily tasks? Never. You must replace the to-do list with Most Important Tasks (MITs). MITs allow you to focus on the most important tasks on your list. You feel progress and accomplishment when you finish these tasks. MITs don't include ad-hoc emails, meetings, etc.

Journal Mapped

Most people don't journal or plan their day in the developing South. I've learned to plan my day in my journal over time. I have multiple sections on one page: MITs (things I want to accomplish that day), Other Activities (stuff I can postpone), Life (health, faith, and family issues), and Pop-Ups (things that just pop up). I leave the next page blank for notes. I reflected on the blocks to identify areas to improve the next day. You will have bad days, but at least you'll realize it was due to poor time management.

Buy time/delegate

Time or money? When you make enough money, you lose time to make more. The smart buy "Time." I resisted buying other people's time for years. I regret not hiring an assistant sooner. Learn to buy time from others and pay for time-consuming tasks. Sometimes you think you're saving money by doing things yourself, but you're actually losing money.

This post is a summary. See the full post here.

Using math to write efficient code in any language

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

Inbuilt max and min functions can minimize verbose if statements.

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.