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Daniel Clery

3 years ago

Twisted device investigates fusion alternatives

More on Science

Tomas Pueyo

Tomas Pueyo

2 years ago

Soon, a Starship Will Transform Humanity

SpaceX's Starship.

Source

Launched last week.

Four minutes in:

SpaceX will succeed. When it does, its massiveness will matter.

Source

Its payload will revolutionize space economics.

Civilization will shift.

We don't yet understand how this will affect space and Earth culture. Grab it.

The Cost of Space Transportation Has Decreased Exponentially

Space launches have increased dramatically in recent years.

We mostly send items to LEO, the green area below:

I always had a hard time remembering that LEO stands for Low-Earth Orbit. Now I imagine a lion orbiting the Earth, and that did the trick.

SpaceX's reusable rockets can send these things to LEO. Each may launch dozens of payloads into space.

With all these launches, we're sending more than simply things to space. Volume and mass. Since the 1980s, launching a kilogram of payload to LEO has become cheaper:

Falcon Heavy is the heavy rocket from SpaceX. Notice this is a logarithmic scale! The Falcon Heavy was SpaceX’s biggest rocket yet. It will soon be superseded by Starship.

One kilogram in a large rocket cost over $75,000 in the 1980s. Carrying one astronaut cost nearly $5M! Falcon Heavy's $1,500/kg price is 50 times lower. SpaceX's larger, reusable rockets are amazing.

SpaceX's Starship rocket will continue. It can carry over 100 tons to LEO, 50% more than the current Falcon heavy. Thousands of launches per year. Elon Musk predicts Falcon Heavy's $1,500/kg cost will plummet to $100 in 23 years.

In context:

Angara was the rocket that previously held the record for cheapest transportation to LEO.

People underestimate this.

2. The Benefits of Affordable Transportation

Compare Earth's transportation costs:

Source: US Department of Transportation.

It's no surprise that the US and Northern Europe are the wealthiest and have the most navigable interior waterways.

The Mississippi River is one of the biggest systems of navigable waterways on Earth. And on top of that, navigation along the US’s Mexican Gulf and East Coast is protected by a series of islands, making sea shipping easier than in the open ocean.European navigable waterways

So what? since sea transportation is cheaper than land. Inland waterways are even better than sea transportation since weather is less of an issue, currents can be controlled, and rivers serve two banks instead of one for coastal transportation.

In France, because population density follows river systems, rivers are valuable. Cheap transportation brought people and money to rivers, especially their confluences.

Look at the population. Can you see dark red lines? Those are people living close to rivers. You can guess where the rivers are by looking at the map. Also, you can see the bigger cities are always at the confluence between rivers.

How come? Why were humans surrounding rivers?

Imagine selling meat for $10 per kilogram. Transporting one kg one kilometer costs $1. Your margin decreases $1 each kilometer. You can only ship 10 kilometers. For example, you can only trade with four cities:

If instead, your cost of transportation is half, what happens? It costs you $0.5 per km. You now have higher margins with each city you traded with. More importantly, you can reach 20-km markets.

However, 2x distance 4x surface! You can now trade with sixteen cities instead of four! Metcalfe's law states that a network's value increases with its nodes squared. Since now sixteen cities can connect to yours. Each city now has sixteen connections! They get affluent and can afford more meat.

Rivers lower travel costs, connecting many cities, which can trade more, get wealthy, and buy more.

The right network is worth at least an order of magnitude more than the left! The cheaper the transport, the more trade at a lower cost, the more income generated, the more that wealth can be reinvested in better canals, bridges, and roads, and the wealth grows even more.

Throughout history. Rome was established around cheap Mediterranean transit and preoccupied with cutting overland transportation costs with their famous roadways. Communications restricted their empire.

This map shows the distance from Rome in terms of days of travel. The size of the Roman Empire was about five weeks of travel. This is not a coincidence. Source: Orbis, the Stanford Geospatial Network Model of the Roman World

The Egyptians lived around the Nile, the Vikings around the North Sea, early Japan around the Seto Inland Sea, and China started canals in the 5th century BC.

Transportation costs shaped empires.Starship is lowering new-world transit expenses. What's possible?

3. Change Organizations, Change Companies, Change the World

Starship is a conveyor belt to LEO. A new world of opportunity opens up as transportation prices drop 100x in a decade.

Satellite engineers have spent decades shedding milligrams. Weight influenced every decision: pricing structure, volumes to be sent, material selections, power sources, thermal protection, guiding, navigation, and control software. Weight was everything in the mission. To pack as much science into every millimeter, NASA missions had to be miniaturized. Engineers were indoctrinated against mass.

No way.

Starship is not constrained by any space mission, robotic or crewed.

Starship obliterates the mass constraint and every last vestige of cultural baggage it has gouged into the minds of spacecraft designers. A dollar spent on mass optimization no longer buys a dollar saved on launch cost. It buys nothing. It is time to raise the scope of our ambition and think much bigger. — Casey Handmer, Starship is still not understood

A Tesla Roadster in space makes more sense.

Starman, the roadster, and the Earth. Source.

It went beyond bad PR. It told the industry: Did you care about every microgram? No more. My rockets are big enough to send a Tesla without noticing. Industry watchers should have noticed.

Most didn’t. Artemis is a global mission to send astronauts to the Moon and build a base. Artemis uses disposable Space Launch System rockets. Instead of sending two or three dinky 10-ton crew habitats over the next decade, Starship might deliver 100x as much cargo and create a base for 1,000 astronauts in a year or two. Why not? Because Artemis remains in a pre-Starship paradigm where each kilogram costs a million dollars and we must aggressively descope our objective.

An overengineer at work

Space agencies can deliver 100x more payload to space for the same budget with 100x lower costs and 100x higher transportation volumes. How can space economy saturate this new supply?

Before Starship, NASA supplied heavy equipment for Moon base construction. After Starship, Caterpillar and Deere may space-qualify their products with little alterations. Instead than waiting decades for NASA engineers to catch up, we could send people to build a space outpost with John Deere equipment in a few years.

History is littered with the wreckage of former industrial titans that underestimated the impact of new technology and overestimated their ability to adapt: Blockbuster, Motorola, Kodak, Nokia, RIM, Xerox, Yahoo, IBM, Atari, Sears, Hitachi, Polaroid, Toshiba, HP, Palm, Sony, PanAm, Sega, Netscape, Compaq, GM… — Casey Handmer, Starship is still not understood

Everyone saw it coming, but senior management failed to realize that adaption would involve moving beyond their established business practice. Others will if they don't.

4. The Starship Possibilities

It's Starlink.

SpaceX invented affordable cargo space and grasped its implications first. How can we use all this inexpensive cargo nobody knows how to use?

Satellite communications seemed like the best way to capitalize on it. They tried. Starlink, designed by SpaceX, provides fast, dependable Internet worldwide. Beaming information down is often cheaper than cable. Already profitable.

Starlink is one use for all this cheap cargo space. Many more. The longer firms ignore the opportunity, the more SpaceX will acquire.

What are these chances?

Satellite imagery is outdated and lacks detail. We can improve greatly. Synthetic aperture radar can take beautiful shots like this:

This radar image acquired by the SIR-C/X-SAR radar on board the Space Shuttle Endeavour shows the Teide volcano. The city of Santa Cruz de Tenerife is visible as the purple and white area on the lower right edge of the island. Lava flows at the summit crater appear in shades of green and brown, while vegetation zones appear as areas of purple, green and yellow on the volcano’s flanks. Source.

Have you ever used Google Maps and thought, "I want to see this in more detail"? What if I could view Earth live? What if we could livestream an infrared image of Earth?

The fall of Kabul. Source: Maxar

We could launch hundreds of satellites with such mind-blowing visual precision of the Earth that we would dramatically improve the accuracy of our meteorological models; our agriculture; where crime is happening; where poachers are operating in the savannah; climate change; and who is moving military personnel where. Is that useful?

What if we could see Earth in real time? That affects businesses? That changes society?

Katherine Kornei

Katherine Kornei

3 years ago

The InSight lander from NASA has recorded the greatest tremor ever felt on Mars.

The magnitude 5 earthquake was responsible for the discharge of energy that was 10 times greater than the previous record holder.

Any Martians who happen to be reading this should quickly learn how to duck and cover.

NASA's Jet Propulsion Laboratory in Pasadena, California, reported that on May 4, the planet Mars was shaken by an earthquake of around magnitude 5, making it the greatest Marsquake ever detected to this point. The shaking persisted for more than six hours and unleashed more than ten times as much energy as the earthquake that had previously held the record for strongest.

The event was captured on record by the InSight lander, which is operated by the United States Space Agency and has been researching the innards of Mars ever since it touched down on the planet in 2018 (SN: 11/26/18). The epicenter of the earthquake was probably located in the vicinity of Cerberus Fossae, which is located more than 1,000 kilometers away from the lander.

The surface of Cerberus Fossae is notorious for being broken up and experiencing periodic rockfalls. According to geophysicist Philippe Lognonné, who is the lead investigator of the Seismic Experiment for Interior Structure, the seismometer that is onboard the InSight lander, it is reasonable to assume that the ground is moving in that area. "This is an old crater from a volcanic eruption."

Marsquakes, which are similar to earthquakes in that they give information about the interior structure of our planet, can be utilized to investigate what lies beneath the surface of Mars (SN: 7/22/21). And according to Lognonné, who works at the Institut de Physique du Globe in Paris, there is a great deal that can be gleaned from analyzing this massive earthquake. Because the quality of the signal is so high, we will be able to focus on the specifics.

Laura Sanders

Laura Sanders

3 years ago

Xenobots, tiny living machines, can duplicate themselves.

Strange and complex behavior of frog cell blobs


A xenobot “parent,” shaped like a hungry Pac-Man (shown in red false color), created an “offspring” xenobot (green sphere) by gathering loose frog cells in its opening.

Tiny “living machines” made of frog cells can make copies of themselves. This newly discovered renewal mechanism may help create self-renewing biological machines.

According to Kirstin Petersen, an electrical and computer engineer at Cornell University who studies groups of robots, “this is an extremely exciting breakthrough.” She says self-replicating robots are a big step toward human-free systems.

Researchers described the behavior of xenobots earlier this year (SN: 3/31/21). Small clumps of skin stem cells from frog embryos knitted themselves into small spheres and started moving. Cilia, or cellular extensions, powered the xenobots around their lab dishes.

The findings are published in the Proceedings of the National Academy of Sciences on Dec. 7. The xenobots can gather loose frog cells into spheres, which then form xenobots.
The researchers call this type of movement-induced reproduction kinematic self-replication. The study's coauthor, Douglas Blackiston of Tufts University in Medford, Massachusetts, and Harvard University, says this is typical. For example, sexual reproduction requires parental sperm and egg cells. Sometimes cells split or budded off from a parent.

“This is unique,” Blackiston says. These xenobots “find loose parts in the environment and cobble them together.” This second generation of xenobots can move like their parents, Blackiston says.
The researchers discovered that spheroid xenobots could only produce one more generation before dying out. The original xenobots' shape was predicted by an artificial intelligence program, allowing for four generations of replication.

A C shape, like an openmouthed Pac-Man, was predicted to be a more efficient progenitor. When improved xenobots were let loose in a dish, they began scooping up loose cells into their gaping “mouths,” forming more sphere-shaped bots (see image below). As many as 50 cells clumped together in the opening of a parent to form a mobile offspring. A xenobot is made up of 4,000–6,000 frog cells.

Petersen likes the Xenobots' small size. “The fact that they were able to do this at such a small scale just makes it even better,” she says. Miniature xenobots could sculpt tissues for implantation or deliver therapeutics inside the body.

Beyond the xenobots' potential jobs, the research advances an important science, says study coauthor and Tufts developmental biologist Michael Levin. The science of anticipating and controlling the outcomes of complex systems, he says.

“No one could have predicted this,” Levin says. “They regularly surprise us.” Researchers can use xenobots to test the unexpected. “This is about advancing the science of being less surprised,” Levin says.

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Scott Galloway

Scott Galloway

3 years ago

Attentive

From oil to attention.

Oil has been the most important commodity for a century. It's sparked wars. Pearl Harbor was a preemptive strike to guarantee Japanese access to Indonesian oil, and it made desert tribes rich. Oil's heyday is over. From oil to attention.

We talked about an information economy. In an age of abundant information, what's scarce? Attention. Scale of the world's largest enterprises, wealth of its richest people, and power of governments all stem from attention extraction, monetization, and custody.

Attention-grabbing isn't new. Humans have competed for attention and turned content into wealth since Aeschylus' Oresteia. The internal combustion engine, industrial revolutions in mechanization and plastics, and the emergence of a mobile Western lifestyle boosted oil. Digitization has put wells in pockets, on automobile dashboards, and on kitchen counters, drilling for attention.

The most valuable firms are attention-seeking enterprises, not oil companies. Big Tech dominates the top 4. Tech and media firms are the sheikhs and wildcatters who capture our attention. Blood will flow as the oil economy rises.

Attention to Detail

More than IT and media companies compete for attention. Podcasting is a high-growth, low-barrier-to-entry chance for newbies to gain attention and (for around 1%) make money. Conferences are good for capturing in-person attention. Salesforce paid $30 billion for Slack's dominance of workplace attention, while Spotify is transforming music listening attention into a media platform.

Conferences, newsletters, and even music streaming are artisan projects. Even 130,000-person Comic Con barely registers on the attention economy's Richter scale. Big players have hundreds of millions of monthly users.

Supermajors

Even titans can be disrupted in the attention economy. TikTok is fracking king Chesapeake Energy, a rule-breaking insurgent with revolutionary extraction technologies. Attention must be extracted, processed, and monetized. Innovators disrupt the attention economy value chain.

Attention pre-digital Entrepreneurs commercialized intriguing or amusing stuff like a newspaper or TV show through subscriptions and ads. Digital storage and distribution's limitless capacity drove the initial wave of innovation. Netflix became dominant by releasing old sitcoms and movies. More ad-free content gained attention. By 2016, Netflix was greater than cable TV. Linear scale, few network effects.

Social media introduced two breakthroughs. First, users produced and paid for content. Netflix's economics are dwarfed by TikTok and YouTube, where customers create the content drill rigs that the platforms monetize.

Next, social media businesses expanded content possibilities. Twitter, Facebook, and Reddit offer traditional content, but they transform user comments into more valuable (addictive) emotional content. By emotional resonance, I mean they satisfy a craving for acceptance or anger us. Attention and emotion are mined from comments/replies, piss-fights, and fast-brigaded craziness. Exxon has turned exhaust into heroin. Should we be so linked without a commensurate presence? You wouldn't say this in person. Anonymity allows fraudulent accounts and undesirable actors, which platforms accept to profit from more pollution.

FrackTok

A new entrepreneur emerged as ad-driven social media anger contaminated the water table. TikTok is remaking the attention economy. Short-form video platform relies on user-generated content, although delivery is narrower and less social.

Netflix grew on endless options. Choice requires cognitive effort. TikTok is the least demanding platform since TV. App video plays when opened. Every video can be skipped with a swipe. An algorithm watches how long you watch, what you finish, and whether you like or follow to create a unique streaming network. You can follow creators and respond, but the app is passive. TikTok's attention economy recombination makes it apex predator. The app has more users than Facebook and Instagram combined. Among teens, it's overtaking the passive king, TV.

Externalities

Now we understand fossil fuel externalities. A carbon-based economy has harmed the world. Fracking brought large riches and rebalanced the oil economy, but at a cost: flammable water, earthquakes, and chemical leaks.

TikTok has various concerns associated with algorithmically generated content and platforms. A Wall Street Journal analysis discovered new accounts listed as belonging to 13- to 15-year-olds would swerve into rabbitholes of sex- and drug-related films in mere days. TikTok has a unique externality: Chinese Communist Party ties. Our last two presidents realized the relationship's perils. Concerned about platform's propaganda potential.

No evidence suggests the CCP manipulated information to harm American interests. A headjack implanted on America's youth, who spend more time on TikTok than any other network, connects them to a neural network that may be modified by the CCP. If the product and ownership can't be separated, the app should be banned. Putting restrictions near media increases problems. We should have a reciprocal approach with China regarding media firms. Ban TikTok

It was a conference theme. I anticipated Axel Springer CEO Mathias Döpfner to say, "We're watching them." (That's CEO protocol.) TikTok should be outlawed in every democracy as an espionage tool. Rumored regulations could lead to a ban, and FCC Commissioner Brendan Carr pushes for app store prohibitions. Why not restrict Chinese propaganda? Some disagree: Several renowned tech writers argued my TikTok diatribe last week distracted us from privacy and data reform. The situation isn't zero-sum. I've warned about Facebook and other tech platforms for years. Chewing gum while walking is possible.

The Future

Is TikTok the attention-economy titans' final evolution? The attention economy acts like it. No original content. CNN+ was unplugged, Netflix is losing members and has lost 70% of its market cap, and households are canceling cable and streaming subscriptions in historic numbers. Snap Originals closed in August after YouTube Originals in January.

Everyone is outTik-ing the Tok. Netflix debuted Fast Laughs, Instagram Reels, YouTube Shorts, Snap Spotlight, Roku The Buzz, Pinterest Watch, and Twitter is developing a TikTok-like product. I think they should call it Vine. Just a thought.

Meta's internal documents show that users spend less time on Instagram Reels than TikTok. Reels engagement is dropping, possibly because a third of the videos were generated elsewhere (usually TikTok, complete with watermark). Meta has tried to downrank these videos, but they persist. Users reject product modifications. Kim Kardashian and Kylie Jenner posted a meme urging Meta to Make Instagram Instagram Again, resulting in 312,000 signatures. Mark won't hear the petition. Meta is the fastest follower in social (see Oculus and legless hellscape fever nightmares). Meta's stock is at a five-year low, giving those who opposed my demands to break it up a compelling argument.

Blue Pill

TikTok's short-term dominance in attention extraction won't be stopped by anyone who doesn't hear Hail to the Chief every time they come in. Will TikTok still be a supermajor in five years? If not, YouTube will likely rule and protect Kings Landing.

56% of Americans regularly watch YouTube. Compared to Facebook and TikTok, 95% of teens use Instagram. YouTube users upload more than 500 hours of video per minute, a number that's likely higher today. Last year, the platform garnered $29 billion in advertising income, equivalent to Netflix's total.

Business and biology both value diversity. Oil can be found in the desert, under the sea, or in the Arctic. Each area requires a specific ability. Refiners turn crude into gas, lubricants, and aspirin. YouTube's variety is unmatched. One-second videos to 12-hour movies. Others are studio-produced. (My Bill Maher appearance was edited for YouTube.)

You can dispute in the comment section or just stream videos. YouTube is used for home improvement, makeup advice, music videos, product reviews, etc. You can load endless videos on a topic or creator, subscribe to your favorites, or let the suggestion algo take over. YouTube relies on user content, but it doesn't wait passively. Strategic partners advise 12,000 creators. According to a senior director, if a YouTube star doesn’t post once week, their manager is “likely to know why.”

YouTube's kevlar is its middle, especially for creators. Like TikTok, users can start with low-production vlogs and selfie videos. As your following expands, so does the scope of your production, bringing longer videos, broadcast-quality camera teams and performers, and increasing prices. MrBeast, a YouTuber, is an example. MrBeast made gaming videos and YouTube drama comments.

Donaldson's YouTube subscriber base rose. MrBeast invests earnings to develop impressive productions. His most popular video was a $3.5 million Squid Game reenactment (the cost of an episode of Mad Men). 300 million people watched. TikTok's attention-grabbing tech is too limiting for this type of material. Now, Donaldson is focusing on offline energy with a burger restaurant and cloud kitchen enterprise.

Steps to Take

Rapid wealth growth has externalities. There is no free lunch. OK, maybe caffeine. The externalities are opaque, and the parties best suited to handle them early are incentivized to construct weapons of mass distraction to postpone and obfuscate while achieving economic security for themselves and their families. The longer an externality runs unchecked, the more damage it causes and the more it costs to fix. Vanessa Pappas, TikTok's COO, didn't shine before congressional hearings. Her comms team over-consulted her and said ByteDance had no headquarters because it's scattered. Being full of garbage simply promotes further anger against the company and the awkward bond it's built between the CCP and a rising generation of American citizens.

This shouldn't distract us from the (still existent) harm American platforms pose to our privacy, teenagers' mental health, and civic dialogue. Leaders of American media outlets don't suffer from immorality but amorality, indifference, and dissonance. Money rain blurs eyesight.

Autocratic governments that undermine America's standing and way of life are immoral. The CCP has and will continue to use all its assets to harm U.S. interests domestically and abroad. TikTok should be spun to Western investors or treated the way China treats American platforms: kicked out.

So rich,

Shalitha Suranga

Shalitha Suranga

3 years ago

The Top 5 Mathematical Concepts Every Programmer Needs to Know

Using math to write efficient code in any language

Photo by Emile Perron on Unsplash, edited with Canva

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.

A mathematical expression/formula in the Linux codebase, a screenshot by the author

Inbuilt max and min functions can minimize verbose if statements.

Reducing a verbose nested-if with the min function in Neutralinojs, a screenshot by the author

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.

GetWindowRect outputs an LPRECT geometric object, a screenshot by the author

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):

The Git codebase defines a function with logarithmic time complexity, a screenshot by the author

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

A utility function that uses ceil, a screenshot by the author

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.

Sad NoCoiner

Sad NoCoiner

3 years ago

Two Key Money Principles You Should Understand But Were Never Taught

Prudence is advised. Be debt-free. Be frugal. Spend less.

This advice sounds nice, but it rarely works.

Most people never learn these two money rules. Both approaches will impact how you see personal finance.

It may safeguard you from inflation or the inability to preserve money.

Let’s dive in.

#1: Making long-term debt your ally

High-interest debt hurts consumers. Many credit cards carry 25% yearly interest (or more), so always pay on time. Otherwise, you’re losing money.

Some low-interest debt is good. Especially when buying an appreciating asset with borrowed money.

Inflation helps you.

If you borrow $800,000 at 3% interest and invest it at 7%, you'll make $32,000 (4%).

As money loses value, fixed payments get cheaper. Your assets' value and cash flow rise.

The never-in-debt crowd doesn't know this. They lose money paying off mortgages and low-interest loans early when they could have bought assets instead.

#2: How To Buy Or Build Assets To Make Inflation Irrelevant

Dozens of studies demonstrate actual wage growth is static; $2.50 in 1964 was equivalent to $22.65 now.

These reports never give solutions unless they're selling gold.

But there is one.

Assets beat inflation.

$100 invested into the S&P 500 would have an inflation-adjusted return of 17,739.30%.

Likewise, you can build assets from nothing.  Doing is easy and quick. The returns can boost your income by 10% or more.

The people who obsess over inflation inadvertently make the problem worse for themselves.  They wait for The Big Crash to buy assets. Or they moan about debt clocks and spending bills instead of seeking a solution.

Conclusion

Being ultra-prudent is like playing golf with a putter to avoid hitting the ball into the water. Sure, you might not slice a drive into the pond. But, you aren’t going to play well either. Or have very much fun.

Money has rules.

Avoiding debt or investment risks will limit your rewards. Long-term, being too cautious hurts your finances.

Disclaimer: This article is for entertainment purposes only. It is not financial advice, always do your own research.