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.

Unleash the power of the Option key ⌥

#1 Open a link in the Private tab first.

Previously, if I needed to open a Safari link in a private window, I would:

• copied the URL with the right click command,

• choose File > New Private Window to open a private window, and

• clicked return after pasting the URL.

I've found a more straightforward way.

Right-clicking a link shows this, right?

Hold option (⌥) for:

Click Open Link in New Private Window while holding.

Finished!

#2. Instead of searching for specific characters, try this

You may use unicode for business or school. Most people Google them when they need them.

That is lengthy!

You can type some special characters just by pressing ⌥ and a key.

For instance

• ⌥+2 -> ™ (Trademark)
• ⌥+0 -> ° (Degree)
• ⌥+G -> © (Copyright)
• ⌥+= -> ≠ (Not equal to)
• ⌥+< -> ≤ (Less than or equal to)
• ⌥+> -> ≥ (Greater then or equal to)
• ⌥+/ -> ÷ (Different symbol for division)

#3 Activate Do Not Disturb silently.

Do Not Disturb when sharing my screen is awkward for me (because people may think Im trying to hide some secret notifications).

Here's another method.

Hold ⌥ and click on Time (at the extreme right on the menu-bar).

Now, DND is activated (secretly!). To turn it off, do it again.

Note: This works only for DND focus.

#4. Resize a window starting from its center

Although this is rarely useful, it is still a hidden trick.

When you resize a window, the opposite edge or corner is used as the pivot, right?

However, if you want to resize it with its center as the pivot, hold while doing so.

#5. Yes, Cut-Paste is available on Macs as well (though it is slightly different).

I call it copy-move rather than cut-paste. This is how it works.

Carry it out.

Choose a file (by clicking on it), then copy it (⌘+C).

Go to a new location on your Mac. Do you use ⌘+V to paste it? However, to move it, press ⌘+⌥+V.

This removes the file from its original location and copies it here. And it works exactly like cut-and-paste on Windows.

#6. Instantly expand all folders

Set your Mac's folders to List view.

Assume you have one folder with multiple subfolders, each of which contains multiple files. And you wanted to look at every single file that was over there.

How would you do?

You're used to clicking the ⌄ glyph near the folder and each subfolder to expand them all, right? Instead, hold down ⌥ while clicking ⌄ on the parent folder.

This is what happens next.

Everything expands.

View/Copy a file's path as an added bonus

If you want to see the path of a file in Finder, select it and hold ⌥, and you'll see it at the bottom for a moment.

To copy its path, right-click on the folder and hold down ⌥ to see this

Click on Copy <"folder name"> as Pathname to do it.

#7 "Save As"

I was irritated by the lack of "Save As" in Pages when I first got a Mac (after 15 years of being a Windows guy).

It was necessary for me to save the file as a new file, in a different location, with a different name, or both.

Unfortunately, I couldn't do it on a Mac.

However, I recently discovered that it appears when you hold ⌥ when in the File menu.

Yay!

A few days ago, I was discussing dall-e with two art and tech pals. One artist acquaintance said she knew a frightened illustrator. Would the ability to create anything with a click derail her career? The artist feared this. My curator friend smiled and said this has always been a dread among artists. When the camera was invented, didn't painters say this? Even in the Instagram era, painting exists.

When art and technology collide, there's room for innovation, experimentation, and fear — especially if the technology replicates or replaces art making. What is art's future with dall-e? How does technology affect music, beyond visual art? Recently, I saw "ABBA Voyage," a holographic ABBA concert in London.

"Abba voyage?" my phone asked in early March. A Gen X friend I met through a fashion blogging ring texted me.

"What's abba Voyage?" I asked while opening my front door with keys and coffee.

We're going! Marti, visiting London, took me to a show.

"Absolutely no ABBA songs here." I responded.

My parents didn't play ABBA much, so I don't know much about them. Dad liked Jimi Hendrix, Cream, Deep Purple, and New Orleans jazz. Marti told me ABBA Voyage was a holographic ABBA show with a live band.

The show was fun, extraordinary fun. Nearly everyone on the dance floor wore wigs, ankle-breaking platforms, sequins, and bellbottoms. I saw some millennials and Zoomers among the boomers.

I was intoxicated by the experience.

Automatons date back to the 18th-century mechanical turk. The mechanical turk was a chess automaton operated by a person. The mechanical turk seemed to perform like a human without human intervention, but it required a human in the loop to work properly.

Humans have used non-humans in entertainment for centuries, such as puppets, shadow play, and smoke and mirrors. A show can have animatronic, technological, and non-technological elements, and a live show can blur real and illusion. From medieval puppet shows to mechanical turks to AI filters, bots, and holograms, entertainment has evolved over time.

I'm not a hologram skeptic, but I'm skeptical of technology, especially since I work with it. I love live performances, I love hearing singers breathe, forget lines, and make jokes. Live shows are my favorite because I love watching performers make mistakes or interact with the audience. ABBA Voyage was different.

Marti and I traveled to Manchester after ABBA Voyage to see Liam Gallagher. Similar but different vibe. Similar in that thousands dressed up for the show. ABBA's energy was dizzying. 90s chic replaced sequins in the crowd. Doc Martens, nylon jackets, bucket hats, shaggy hair. The Charlatans and Liam Gallagher opened and closed, respectively. Fireworks. Incredible. People went crazy. Yelling exhausted my voice.

This week in music featured AI-enabled holograms and a decades-old rocker. Both are warm and gooey in our memories.

After seeing both, I'm wondering if we need AI hologram shows. Why? Is it good?

Like everything tech-related, my answer is "maybe." Because context and performance matter. Liam Gallagher and ABBA both had great, different shows.

For a hologram to work, it must be impossible and big. It must be big, showy, and improbable to justify a hologram. It must feel...expensive, like a stadium pop show. According to a quick search, ABBA broke up on bad terms. Reuniting is unlikely. This is also why Prince or Tupac hologram shows work. We can only engage with their legacy through covers or...holograms.

I drove around listening to the radio a few weeks ago. "Dreaming of You" by Selena played. Selena's music defined my childhood. I sang along and turned up the volume (or as loud as my husband would allow me while driving on the highway).

I discovered Selena's music six months after her death, so I never saw her perform live. My babysitter Melissa played me her album after I moved to Houston. Melissa took me to see the Selena movie five times when it came out. I quickly wore out my VHS copy. I constantly sang "Bibi Bibi Bom Bom" and "Como la Flor." I love Selena. A Selena hologram? Yes, probably.

Instagram advertised a cellist's Arthur Russell tribute show. Russell is another deceased artist I love. I almost walked down the aisle to "This is How We Walk on the Moon," but our cellist couldn't find it. Instead, I walked to Magnetic Fields' "The Book of Love." I "discovered" Russell after a friend introduced me to his music a few years ago.

I use these as analogies for the Liam Gallagher and ABBA concerts.

You have no idea how much I'd pay to see a hologram of Selena's 1995 Houston Livestock Show and Rodeo concert. Arthur Russell's hologram is unnecessary. Russell's work was intimate and performance-based. We can't separate his life from his legacy; popular audiences overlooked his genius. He died of AIDS broke. Like Selena, he died prematurely. Given his music and history, another performer would be a better choice than a hologram. He's no Selena. Selena could have rivaled Beyonce.

Pop shows' size works for holograms. Along with ABBA holograms, there was an anime movie and a light show that would put Tron to shame. ABBA created a tourable stadium show. The event was lavish, expensive, and well-planned. Pop, unlike rock, isn't gritty. Liam Gallagher hologram? No longer impossible, it wouldn't work. He's touring. I'm not sure if a rockstar alone should be rendered as a hologram; it was the show that made ABBA a hologram.

Holograms, like AI, are part of the future of entertainment, but not all of it. Because only modern interpretations of Arthur Russell's work reveal his legacy. That's his legacy.

Large-scale arena performers may use holograms in the future, but the experience must be impossible. A teacher once said that the only way to convey emotion in opera is through song, and I feel the same way about holograms, AR, VR, and mixed reality. A story's impossibility must make sense, like in opera. Impossibility and bombastic performance must be present for an immersive element to "work." ABBA was an impossible and improbable experience, which made it magical. It helped the holographic show work.

Marti told me about ABBA Voyage. She said it was a great concert. Marti has worked in music since the 1990s. She's a music expert; she's seen many shows.

Ai isn't a god or sentient, and the ABBA holograms aren't real. The renderings were glassy-eyed, flat, and robotic, like the Polar Express or the Jaws shark. Even today, the uncanny valley is insurmountable. We know it's not real because it's not about reality. It was about a suspended moment and performance feelings.

I knew this was impossible, an 'unreal' experience, but the emotions I felt were real, like watching a movie or tv show. Perhaps this is one of the better uses of AI, like CGI and special effects, like the beauty of entertainment- we were enraptured and entertained for hours. I've been playing ABBA since then.

Peter Thiel studied philosophy as an undergraduate.

Peter Thiel has $7.36 billion.

Peter is a world-ranked chess player, has a legal degree, and has written profitable novels.

In 1999, he co-founded PayPal with Max Levchin, which merged with X.com.

Peter Thiel made $55 million after selling the company to eBay for $1.5 billion in 2002.

You may be wondering…

How did Peter turn $55 million into his now multi-billion dollar net worth?

One amazing investment?

Facebook.

Thiel was Facebook's first external investor. He bought 10% of the company for $500,000 in 2004.

This investment returned 159% annually, 200x in 8 years.

By 2012, Thiel sold almost all his Facebook shares, becoming a billionaire.

What was the investment thesis of Peter?

This investment appeared ridiculous. Facebook was an innovative startup.

Thiel's $500,000 contribution transformed Facebook.

Harvard students have access to Facebook's 8 features and 1 photo per profile.

How did Peter determine that this would be a wise investment, then?

Facebook is a mimetic desire machine.

Social media's popularity is odd. Why peek at strangers' images on a computer?

Peter Thiel studied under French thinker Rene Girard at Stanford.

Mimetic Desire explains social media's success.

Mimetic Desire is the idea that humans desire things simply because other people do.

If nobody wanted it, would you?

Would you desire a family, a luxury car, or expensive clothes if no one else did? Girard says no.

People we admire affect our aspirations because we're social animals. Every person has a role model.

Our nonreligious culture implies role models are increasingly other humans, not God.

The idea explains why social media influencers are so powerful.

Why would Andrew Tate or Kim Kardashian matter if people weren't mimetic?

Humanity is fundamentally motivated by social comparison.

Facebook takes advantage of this need for social comparison, and puts it on a global scale.

It aggregates photographs and updates from millions of individuals.

Facebook mobile allows 24/7 social comparison.

Thiel studied mimetic desire with Girard and realized Facebook exploits the urge for social comparison to gain money.

Social media is more significant and influential than ever, despite Facebook's decline.

Thiel and Girard show that applied philosophy (particularly in business) can be immensely profitable.

I read 1k+ page 3AC liquidation documentation so you don't have to. Also sharing revised Celsius recovery plans.

3AC's liquidation documents:

Someone disclosed 3AC liquidation records in the BVI courts recently. I'll discuss the leak's timeline and other highlights.

Three Arrows Capital began trading traditional currencies in emerging markets in 2012. They switched to equities and crypto, then purely crypto in 2018.

By 2020, the firm had $703mm in net assets and $1.8bn in loans (these guys really like debt).

The firm's net assets under control reached $3bn in April 2022, according to the filings. 3AC had $600mm of LUNA/UST exposure before May 9th 2022, which put them over.

LUNA and UST go to zero quickly (I wrote about the mechanics of the blowup here). Kyle Davies, 3AC co-founder, told Blockchain.com on May 13 that they have $2.4bn in assets and $2.3bn NAV vs. $2bn in borrowings. As BTC and ETH plunged 33% and 50%, the company became insolvent by mid-2022.

3AC sent $32mm to Tai Ping Shen, a Cayman Islands business owned by Su Zhu and Davies' partner, Kelly Kaili Chen (who knows what is going on here).

3AC had borrowed over $3.5bn in notional principle, with Genesis ($2.4bn) and Voyager ($650mm) having the most exposure.

Genesis demanded $355mm in further collateral in June.

Deribit (another 3AC investment) called for $80 million in mid-June.

Even in mid-June, the corporation was trying to borrow more money to stay afloat. They approached Genesis for another $125mm loan (to pay another lender) and HODLnauts for BTC & ETH loans.

Pretty crazy. 3AC founders used borrowed money to buy a $50 million boat, according to the leak.

Su requesting for $5m + Chen Kaili Kelly asserting they loaned $65m unsecured to 3AC are identified as creditors.

Celsius:

This bankruptcy presentation shows the Celsius breakdown from March to July 14, 2022. From $22bn to $4bn, crypto assets plummeted from $14.6bn to $1.8bn (ouch). $16.5bn in user liabilities dropped to $4.72bn.

In my recent post, I examined if "forced selling" is over, with Celsius' crypto assets being a major overhang. In this presentation, it looks that Chapter 11 will provide clients the opportunity to accept cash at a discount or remain long crypto. Provided that a fresh source of money is unlikely to enter the Celsius situation, cash at a discount or crypto given to customers will likely remain a near-term market risk - cash at a discount will likely come from selling crypto assets, while customers who receive crypto could sell at any time. I'll share any Celsius updates I find.

Conclusion

Only Celsius and the Mt Gox BTC unlock remain as forced selling catalysts. While everything went through a "relief" pump, with ETH up 75% from the bottom and numerous alts multiples higher, there are still macro dangers to equities + risk assets. There's a lot of wealth waiting to be deployed in crypto ($153bn in stables), but fund managers are risk apprehensive (lower than 2008 levels).

We're hopefully over crypto's "bottom," with peak anxiety and forced selling behind us, but we may chop around.

To see the full article, click here.