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.

Wish you more bang for your buck

By ‘Cost a Bomb’ I didn’t mean to exaggerate. It’s an idiom that means ‘To be very expensive’. In fact, no app on the planet costs a bomb lol.

So, to the point.

Chronicle

(Freemium. For Pro, $24.99 | Available on Setapp)

You probably have trouble keeping track of dozens of bills and subscriptions each month.

Try Chronicle.

Easy-to-use app

• Add payment due dates and receive reminders,

• Save payment documentation,

• Analyze your spending by season, year, and month.

• Observe expenditure trends and create new budgets.

Best of all, Chronicle features an integrated browser for fast payment and logging.

iOS and macOS sync.

SoundSource

($39 for lifetime)

Background Music, a free macOS program, was featured in #6 of this post last month.

It controls per-app volume, stereo balance, and audio over its max level.

Background Music is fully supported. Additionally,

• Connect various speakers to various apps (Wow! ),

• change the audio sample rate for each app,

• To facilitate access, add a floating SoundSource window.

• Use its blocks in Shortcuts app,

• On the menu bar, include meters for output/input devices and running programs.

PixelSnap

($39 for lifetime | Available on Setapp)

This software is heaven for UI designers.

It aids you.

• quickly calculate screen distances (in pixels) ,

• Drag an area around an object to determine its borders,

• Measure the distances between the additional guides,

• screenshots should be pixel-perfect.

What’s more.

You can

• Adapt your tolerance for items with poor contrast and shadows.

• Use your Touch Bar to perform important tasks, if you have one.

Mate Translation

($3.99 a month / $29.99 a year | Available on Setapp)

Mate Translate resembles a roided-up version of BarTranslate, which I wrote about in #1 of this piece last month.

If you translate often, utilize Mate Translate on macOS and Safari.

I'm really vocal about it.

It stays on the menu bar, and is accessible with a click or ⌥+shift+T hotkey.

It lets you

• Translate in 103 different languages,

• To translate text, double-click or right-click on it.

• Totally translate websites. Additionally, Netflix subtitles,

• Listen to their pronunciation to see how close it is to human.

iPhone and Mac sync Mate-ing history.

Swish

($16 for lifetime | Available on Setapp)

Swish is awesome!

Swipe, squeeze, tap, and hold movements organize chaotic desktop windows. Swish operates with mouse and trackpad.

Some gestures:

• Pinch Once: Close an app
• Pinch Twice: Quit an app
• Swipe down once: Minimise an app
• Pinch Out: Enter fullscreen mode
• Tap, Hold, & Swipe: Arrange apps in grids
and many more...

After getting acquainted to the movements, your multitasking will improve.

Unite

($24.99 for lifetime | Available on Setapp)

It turns webapps into macOS apps. The end.

Unite's functionality is a million times better.

• Provide extensive customization (incl. its icon, light and dark modes)

• make menu bar applications,

• Get badges for web notifications and automatically refresh websites,

• Replace any dock icon in the window with it (Wow!) by selecting that portion of the window.

• Use PiP (Picture-in-Picture) on video sites that support it.

• Delete advertising,

• Throughout macOS, use floating windows

and many more…

I feel $24.99 one-off for this tool is a great deal, considering all these features. What do you think?

https://www.bzgapps.com/unite

CleanShot X

(Basic: $29 one-off. Pro: $8/month | Available on Setapp)

CleanShot X can achieve things the macOS screenshot tool cannot. Complete screenshot toolkit.

CleanShot X, like Pixel Snap 2 (#3), is fantastic.

Allows

• Scroll to capture a long page,

• screen recording,

  With webcam on,
• With mic and system audio,
• Highlighting mouse clicks and hotkeys.

• Maintain floating screenshots for reference

• While capturing, conceal desktop icons and notifications.

• Recognize text in screenshots (OCR),

• You may upload and share screenshots using the built-in cloud.

These are just 6 in 50+ features, and you’re already saying Wow!

Recent investigations have shown that generative AI can boost hackers and misinformation spreaders.

Since its inception in late November 2022, OpenAI's ChatGPT has entertained and assisted many online users in writing, coding, task automation, and linguistic translation. Given this versatility, it is maybe unsurprising but nonetheless regrettable that fraudsters and mis-, dis-, and malinformation (MDM) spreaders are also considering ChatGPT and related AI models to streamline and improve their operations.

Malign actors may benefit from ChatGPT, according to a WithSecure research. ChatGPT promises to elevate unlawful operations across many attack channels. ChatGPT can automate spear phishing attacks that deceive corporate victims into reading emails from trusted parties. Malware, extortion, and illicit fund transfers can result from such access.

ChatGPT's ability to simulate a desired writing style makes spear phishing emails look more genuine, especially for international actors who don't speak English (or other languages like Spanish and French).

This technique could let Russian, North Korean, and Iranian state-backed hackers conduct more convincing social engineering and election intervention in the US. ChatGPT can also create several campaigns and various phony online personas to promote them, making such attacks successful through volume or variation. Additionally, image-generating AI algorithms and other developing techniques can help these efforts deceive potential victims.

Hackers are discussing using ChatGPT to install malware and steal data, according to a Check Point research. Though ChatGPT's scripts are well-known in the cyber security business, they can assist amateur actors with little technical understanding into the field and possibly develop their hacking and social engineering skills through repeated use.

Additionally, ChatGPT's hacking suggestions may change. As a writer recently indicated, ChatGPT's ability to blend textual and code-based writing might be a game-changer, allowing the injection of innocent content that would subsequently turn out to be a malicious script into targeted systems. These new AI-powered writing- and code-generation abilities allow for unique cyber attacks, regardless of viability.

OpenAI fears ChatGPT usage. OpenAI, Georgetown University's Center for Security and Emerging Technology, and Stanford's Internet Observatory wrote a paper on how AI language models could enhance nation state-backed influence operations. As a last resort, the authors consider polluting the internet with radioactive or misleading data to ensure that AI language models produce outputs that other language models can identify as AI-generated. However, the authors of this paper seem unaware that their "solution" might cause much worse MDM difficulties.

Literally False News

The public argument about ChatGPTs content-generation has focused on originality, bias, and academic honesty, but broader global issues are at stake. ChatGPT can influence public opinion, troll individuals, and interfere in local and national elections by creating and automating enormous amounts of social media material for specified audiences.

ChatGPT's capacity to generate textual and code output is crucial. ChatGPT can write Python scripts for social media bots and give diverse content for repeated posts. The tool's sophistication makes it irrelevant to one's language skills, especially English, when writing MDM propaganda.

I ordered ChatGPT to write a news piece in the style of big US publications declaring that Ukraine is on the verge of defeat in its fight against Russia due to corruption, desertion, and exhaustion in its army. I also gave it a fake reporter's byline and an unidentified NATO source's remark. The outcome appears convincing:

Worse, terrible performers can modify this piece to make it more credible. They can edit the general's name or add facts about current wars. Furthermore, such actors can create many versions of this report in different forms and distribute them separately, boosting its impact.

In this example, ChatGPT produced a news story regarding (fictional) greater moviegoer fatality rates:

Editing this example makes it more plausible. Dr. Jane Smith, the putative author of the medical report, might be replaced with a real-life medical person or a real victim of this supposed medical hazard.

Can deceptive texts be found? Detecting AI text is behind AI advancements. Minor AI-generated text alterations can upset these technologies.

Some OpenAI individuals have proposed covert methods to watermark AI-generated literature to prevent its abuse. AI models would create information that appears normal to humans but would follow a cryptographic formula that would warn other machines that it was AI-made. However, security experts are cautious since manually altering the content interrupts machine and human detection of AI-generated material.

How to Prepare

Cyber security and IT workers can research and use generative AI models to fight spear fishing and extortion. Governments may also launch MDM-defence projects.

In election cycles and global crises, regular people may be the most vulnerable to AI-produced deceit. Until regulation or subsequent technical advances, individuals must recognize exposure to AI-generated fraud, dating scams, other MDM activities.

A three-step verification method of new material in suspicious emails or social media posts can help identify AI content and manipulation. This three-step approach asks about the information's distribution platform (is it reliable? ), author (is the reader familiar with them? ), and plausibility given one's prior knowledge of the topic.

Consider a report by a trusted journalist that makes shocking statements in their typical manner. AI-powered fake news may be released on an unexpected platform, such as a newly created Facebook profile. However, if it links to a known media source, it is more likely to be real.

Though hard and subjective, this verification method may be the only barrier against manipulation for now.

AI language models:

How to Recognize an AI-Generated Article ChatGPT, the popular AI-powered chatbot, can and likely does generate medium.com-style articles.

AI-Generated Text Detectors Fail. Do This. Online tools claim to detect ChatGPT output. Even with superior programming, I tested some of these tools. pub

Why Original Writers Matter Despite AI Language Models Creative writers may never be threatened by AI language models.

The Kardashev scale grades civilizations from Type 1 to Type 3 based on energy harvesting.

How do technologically proficient civilizations emerge across timescales measuring in the tens of thousands or even millions of years? This is a question that worries me as a researcher in the search for “technosignatures” from other civilizations on other worlds. Since it is already established that longer-lived civilizations are the ones we are most likely to detect, knowing something about their prospective evolutionary trajectories could be translated into improved search tactics. But even more than knowing what to seek for, what I really want to know is what happens to a society after so long time. What are they capable of? What do they become?

This was the question Russian SETI pioneer Nikolai Kardashev asked himself back in 1964. His answer was the now-famous “Kardashev Scale.” Kardashev was the first, although not the last, scientist to try and define the processes (or stages) of the evolution of civilizations. Today, I want to launch a series on this question. It is crucial to technosignature studies (of which our NASA team is hard at work), and it is also important for comprehending what might lay ahead for mankind if we manage to get through the bottlenecks we have now.

The Kardashev scale

Kardashev’s question can be expressed another way. What milestones in a civilization’s advancement up the ladder of technical complexity will be universal? The main notion here is that all (or at least most) civilizations will pass through some kind of definable stages as they progress, and some of these steps might be mirrored in how we could identify them. But, while Kardashev’s major focus was identifying signals from exo-civilizations, his scale gave us a clear way to think about their evolution.

The classification scheme Kardashev employed was not based on social systems of ethics because they are something that we can probably never predict about alien cultures. Instead, it was built on energy, which is something near and dear to the heart of everybody trained in physics. Energy use might offer the basis for universal stages of civilisation progression because you cannot do the work of establishing a civilization without consuming energy. So, Kardashev looked at what energy sources were accessible to civilizations as they evolved technologically and used those to build his scale.

From Kardashev’s perspective, there are three primary levels or “types” of advancement in terms of harvesting energy through which a civilization should progress.

Type 1: Civilizations that can capture all the energy resources of their native planet constitute the first stage. This would imply capturing all the light energy that falls on a world from its host star. This makes it reasonable, given solar energy will be the largest source available on most planets where life could form. For example, Earth absorbs hundreds of atomic bombs’ worth of energy from the Sun every second. That is a rather formidable energy source, and a Type 1 race would have all this power at their disposal for civilization construction.

Type 2: These civilizations can extract the whole energy resources of their home star. Nobel Prize-winning scientist Freeman Dyson famously anticipated Kardashev’s thinking on this when he imagined an advanced civilization erecting a large sphere around its star. This “Dyson Sphere” would be a machine the size of the complete solar system for gathering stellar photons and their energy.

Type 3: These super-civilizations could use all the energy produced by all the stars in their home galaxy. A normal galaxy has a few hundred billion stars, so that is a whole lot of energy. One way this may be done is if the civilization covered every star in their galaxy with Dyson spheres, but there could also be more inventive approaches.

Implications of the Kardashev scale

Climbing from Type 1 upward, we travel from the imaginable to the god-like. For example, it is not hard to envisage utilizing lots of big satellites in space to gather solar energy and then beaming that energy down to Earth via microwaves. That would get us to a Type 1 civilization. But creating a Dyson sphere would require chewing up whole planets. How long until we obtain that level of power? How would we have to change to get there? And once we get to Type 3 civilizations, we are virtually thinking about gods with the potential to engineer the entire cosmos.

For me, this is part of the point of the Kardashev scale. Its application for thinking about identifying technosignatures is crucial, but even more strong is its capacity to help us shape our imaginations. The mind might become blank staring across hundreds or thousands of millennia, and so we need tools and guides to focus our attention. That may be the only way to see what life might become — what we might become — once it arises to start out beyond the boundaries of space and time and potential.

This is a summary. Read the full article here.

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.

Traditional sales organizations used the concept of a sales “funnel” to describe the process through which potential customers move, ending up with sales at the end. Winners today have abandoned that way of thinking in favor of building flywheels — business models in which every element reinforces every other.

Ah, the marketing funnel…

Prospective clients go through a predictable set of experiences, students learn in business school marketing classes. It looks like this:

Understanding the funnel helps evaluate sales success indicators. Gail Goodwin, former CEO of small business direct mail provider Constant Contact, said managing the pipeline was key to escaping the sluggish SaaS ramp of death.

Like the funnel concept. To predict how well your business will do, measure how many potential clients are aware of it (awareness) and how many take the next step. If 1,000 people heard about your offering and 10% showed interest, you'd have 100 at that point. If 50% of these people made buyer-like noises, you'd know how many were, etc. It helped model buying trends.

TV, magazine, and radio advertising are pricey for B2C enterprises. Traditional B2B marketing involved armies of sales reps, which was expensive and a barrier to entry.

Cracks in the funnel model

Digital has exposed the funnel's limitations. Hubspot was born at a time when buyers and sellers had huge knowledge asymmetries, according to co-founder Brian Halligan. Those selling a product could use the buyer's lack of information to become a trusted partner.

As the world went digital, getting information and comparing offerings became faster, easier, and cheaper. Buyers didn't need a seller to move through a funnel. Interactions replaced transactions, and the relationship didn't end with a sale.

Instead, buyers and sellers interacted in a constant flow. In many modern models, the sale is midway through the process (particularly true with subscription and software-as-a-service models). Example:

You're creating a winding journey with many touch points, not a funnel (and lots of opportunities for customers to get lost).

From winding journey to flywheel

Beyond this revised view of an interactive customer journey, a company can create what Jim Collins famously called a flywheel. Imagine rolling a heavy disc on its axis. The first few times you roll it, you put in a lot of effort for a small response. The same effort yields faster turns as it gains speed. Over time, the flywheel gains momentum and turns without your help.

Modern digital organizations have created flywheel business models, in which any additional force multiplies throughout the business. The flywheel becomes a force multiplier, according to Collins.

Amazon is a famous flywheel example. Collins explained the concept to Amazon CEO Jeff Bezos at a corporate retreat in 2001. In The Everything Store, Brad Stone describes in his book The Everything Store how he immediately understood Amazon's levers.

The result (drawn on a napkin):

Low prices and a large selection of products attracted customers, while a focus on customer service kept them coming back, increasing traffic. Third-party sellers then increased selection. Low-cost structure supports low-price commitment. It's brilliant! Every wheel turn creates acceleration.

Where from here?

Flywheel over sales funnel! Consider these business terms.