More on Technology

Mark Schaefer
3 years ago
20 Fun Uses for ChatGPT
Our RISE community is stoked on ChatGPT. ChatGPT has countless uses.
Early on. Companies are figuring out the legal and ethical implications of AI's content revolution. Using AI for everyday tasks is cool.
So I challenged RISE friends... Let's have fun and share non-obvious uses.
Onward!
1. Tweet
Jim MacLeod requested a design-themed Twitter thread from ChatGPT.
2. Novelize
Giuseppe Fratoni writes novels.
"This is amazing!" Impotent. I asked about writing, mystery novels, and jazz.
"Develop a mystery novel plot in which a disillusioned homicide detective hunts a serial killer who targets jazz musicians who play Autumn Leaves."
"I have:
Detective James Thompson is a seasoned veteran of the Homicide department, but lately he’s been feeling burnt out and disillusioned. His latest case, the murder of a young jazz pianist who was found brutally killed in his home, only serves to deepen his sense of despair … (much more provided)
3. Question-and-answer sessions
Bliss recommends:
You have a guest speaker and want to ask audience questions.
Pre-generate questions with ChatGPT. "And here's a question from our AI?"
The conference is about Western water scarcity. Water management expert. My AI question was...
Which desalination-related questions should I ask an expert?
ChatGPT said...
How is desalination currently being used around the world, and in what types of locations is it most effective?
What are the potential advantages and disadvantages of using desalination to provide fresh water?
What are some of the key challenges and limitations of desalination technology, and how are they being addressed?
4. Game-making
Richard's a board game expert. He suggests using ChatGPT to plan games. Note: Some people have started getting help solving crossword puzzle clues.
5. Matchmaking
Tanya Thompson thinks it helps dating. ChatGPT:
Here are some flirty first-message ideas for dating apps:
I noticed you from afar. I had to say hi and see if we clicked.
Your profile picture is gorgeous. I'm obsessed with your [Feature] and want to know you better.
I don't usually message first, but I had to. You're [Attractive Quality] and I can't wait to talk.”
Hello. Your profile intimidates me. I'm starstruck by your [Attractiveness]. (Many instances)
5. Solitude/anxiety
ChatGPT excels at one-on-one conversations.
PepperBrooks: "I'm sad and lonely."
ChatGPT: I’m sorry to hear that you’re feeling sad and lonely. It’s natural to feel down sometimes, but it’s important to remember that you’re not alone. There are many people who care about you and want to help you. It can be helpful to talk to someone about your feelings, whether it’s a close friend, family member, or mental health professional.
Sometimes, just expressing your thoughts and emotions to someone else can help to alleviate your sadness and loneliness. It’s also important to take care of yourself and do things that make you happy, such as spending time with loved ones, pursuing a hobby, or exercising. These things can help to improve your mood and make you feel more connected to others. Remember that you are strong and capable, and that you can get through this difficult time.
Daniel Nestle asked ChatGPT to generate journal prompts to help him deal with anxiety.
Write down the things that are causing you anxiety at the moment.
Describe a situation in which you felt anxious and how you coped with it.
Reflect on how your thoughts and beliefs contribute to your anxiety.
Write a letter to your anxiety, expressing your feelings and concerns
Imagine yourself in a calm and peaceful place, and describe it in detail.
(many more items followed)
6. Names
Continued Daniel:
Also, naming ideas.
Me: Name this drink. Japanese gin, unsweetened tonic, lime, Szechuan pepper, grapefruit.
ChatGPT: How about “Sakura Sunrise?” The name incorporates the Japanese gin and the citrus flavors of grapefruit and lime, and the word “sunrise” suggests a fresh and invigorating start to the day. Alternatively, you could go with something like “Peppered Grapefruit Gin Fizz” to emphasize the unique flavor combination of Szechuan pepper and grapefruit.
7. Translation on the go
Monks recommends: ChatGPT is a perfect mobile translation tool. Say you need help in Italy.
ME: Translate to Italian
Where is the nearest gas station?
ChatGPT: “La mia auto sta per esaurire il carburante, mi puoi dire dove si trova la stazione di servizio più vicina?”
8. Fitness
Monks added:
ME: In 3 months, I want to run 5km. Plan out how I can do this.
ChatGPT: Here's a 3-month plan to run 5km.
Start by walking for 15–20 minutes each day to build up your endurance and get your body used to regular exercise.
After a week of walking, begin incorporating short jogs into your routine. Start by jogging for 1–2 minutes at a time, with walking breaks in between. Gradually increase the length of your jogs and reduce the amount of time you spend walking.
Once you can jog for 10 minutes without stopping, start increasing the distance of your runs. Aim to run 1km without stopping and then gradually increase the distance over time.
In addition to your regular runs, incorporate strength training and stretching into your routine to improve your overall fitness and reduce the risk of injury.
(more details continued on)
9. Integrations and coding
10. Teacher lesson plans
Spencer Crandall saved time.
This morning, I wondered who has the hardest job. Teachers.
Many students, little time. ChatGPT could handle lesson planning. I tried it and got this.
Lesson Title: The History and Impact of Artificial Intelligence
Students will understand the history and development of AI and the potential positive and negative impacts on society.
AI timeline AI technologies and applications
Overview:
Introduce the topic of artificial intelligence, and explain that it refers to the development of computer systems and algorithms that can simulate human intelligence and behavior.
Show the timeline of significant events in the history of AI, and discuss the key milestones and developments in the field.
Show examples of AI technologies and applications, and explain how they are used in various industries and fields.
Discuss the potential positive and negative impacts of AI on society, including its potential to improve productivity, efficiency, and safety, as well as its potential to create new challenges and concerns, such as job displacement and ethical issues.
(many more details followed)
11. Find podcast guests.
Joeri Billast suggested:
Who should be on my Web3 podcast?
ChatGPT: Web3 marketing experts, influencers, and thought leaders make great podcast guests. These include Web3 marketers, content creators, business owners, entrepreneurs, and technologists. You could invite Web3 startups and organizations to your podcast.
Please give examples.
ChatGPT: Ideal Web3 marketing podcast guests include:
Tim Berner-Lee, inventor of the World Wide Web
Chris Dixon, general partner at Andreessen Horowitz
Vitalik Buterin, founder of Ethereum
Joe Lubin, founder of ConsenSys
Susan Fowler, author of Whistleblower
(many other suggestions)
12. Comments and reviews on social media
Lisa Monk thinks ChatGPT can help retail staff with social media.
She asked ChatGPT to "review this restaurant"
POSITIVE CUSTOMER REVIEW: I absolutely love this place. We eat out a lot however this place has topped it all. Perfect meals, amazing staff and the timing for it all was great! Special thanks to Sophie B (you rock) From your guests all the way from the Gold Coast, THANK YOU
ChatGPT REPLY: Thank you so much for your kind words and for taking the time to write a review. We are delighted to hear that you had such a great experience at our restaurant. We are thrilled that you enjoyed your meal and the service provided by Sophie. It’s always a pleasure to serve guests visiting from the Gold Coast and we are grateful for your support. We look forward to welcoming you back again soon. Thank you again for your positive review.
CUSTOMER REVIEW: Most average food, there is a nice view, But that’s about it
ChatGPT: Thank you for your review. We apologize if your dining experience was not up to your expectations. We strive to provide top-quality food and service to all of our customers, and we will take your feedback into consideration as we continue to improve. Thank you for letting us know about your experience.
13. Crime-fighting
Zack Seipert said, "I researched some famous unsolved murders, and ChatGPT laid out the crime, suspects, clues, and more." I bet experienced detectives could solve some of these cold cases.
14. Reduce bias
Joanne Taylor struggles to remove biases from her writing. She asked ChatGPT for ideas.
I asked ChatGPT to check a text for racial bias, and it did well.
15. Furnishings
I designed a small, unique table using ChatGPT and MidJourney. I edited ChatGPT's idea for clarity and brevity before entering it in MidJourney.
Results:
16. Serialize a novel
Scott Scowcoft led ChatCPT through iterations of a story text to create serialized novel frames. You can view this here.
17. Interview preparation
I was on a sales podcast. Although this is marketing-related, it's not my forte. I asked ChatGPT for help with a sales interview. Response:
Here are some interview questions about the future of sales and how to answer them.
How will technology affect sales in the future?
Technology will impact sales in the coming years. Automation and AI could be used to handle routine tasks, and data analysis and CRM could become more important. E-commerce and online sales channels are also reshaping the sales landscape.
How will the salesperson's role change?
Future sales roles may change in response to changing customer needs and expectations. Salespeople must be knowledgeable and consultative to help customers navigate complex products and services. Increasing importance of data analysis and CRM tools will require salespeople to understand and use technology effectively.
Future sales professionals will need what skills?
Future salespeople will need many skills. Sales professionals must have strong communication and interpersonal skills, as well as product and service knowledge and the ability to use data analysis and CRM tools effectively. Adapting to changing customer needs and staying current on industry trends will also be important for sales success.
18. Gift ideas
I need Christmas gift ideas for my wife. I asked:
Suggest a gift idea under $200 for a middle-aged woman who loves The Eagles.
A middle-aged woman who loves The Eagles might like a vinyl record of "Hotel California" or "The Long Run." Many music fans enjoy the unique sound and experience of vinyl records.
Pair the record with a high-quality record player for a complete gift. The vinyl record and record player should fit within your $200 budget for an Eagles fan.
19. Explaining complex concepts
I entered: Explain quantum physics to me as if I were 10 years old.
Quantum physics is a branch of science that studies how tiny particles, like atoms and subatomic particles, behave. These particles are so small that they don’t always follow the same rules as the things we can see and touch every day.
For example, sometimes they can be in two places at the same time, or they can be friends with each other even if they are far apart. This might sound strange, but it’s what scientists have learned from studying these tiny particles. Quantum physics helps us understand how the world works at a very small scale, and it can also help us make new technologies, like computers that are much faster than the ones we have today.
20. AP-style editing
Blogs, journals, and books follow AP Style. I asked ChatGPT to "edit using AP Style" and it did a great job.
And then... "Write a catchy headline for a blog post about 16 ChatGPT uses"
Here are some possible blog post titles for 20 creative ChatGPT uses:
“20 Fun and Creative Ways to Use ChatGPT: From Games to Quizzes and More”
“The Ultimate Guide to Using ChatGPT for Entertainment and Creativity”
“20 Reasons to Use ChatGPT: How it Can Enhance Your Gaming, Storytelling, and More”
20 Entertaining Uses for ChatGPT You Never Knew Were Possible”
“Unleash Your Imagination with ChatGPT: 16 Creative and Fun Ways to Use it”
In a previous post, I said ChatGPT will change marketing careers forever. I have never made a statement like that in my life. Even in the early days of the internet, people were cautious.
This technology was just released two weeks ago, and over a million people are already using it. This is the fastest technology adoption in history.
Today's post offers inventive and entertaining ideas, but it's just the beginning. ChatGPT writes code, music, and papers.
Thomas Smith
3 years ago
ChatGPT Is Experiencing a Lightbulb Moment
Why breakthrough technologies must be accessible
ChatGPT has exploded. Over 1 million people have used the app, and coding sites like Stack Overflow have banned its answers. It's huge.
I wouldn't have called that as an AI researcher. ChatGPT uses the same GPT-3 technology that's been around for over two years.
More than impressive technology, ChatGPT 3 shows how access makes breakthroughs usable. OpenAI has finally made people realize the power of AI by packaging GPT-3 for normal users.
We think of Thomas Edison as the inventor of the lightbulb, not because he invented it, but because he popularized it.
Going forward, AI companies that make using AI easy will thrive.
Use-case importance
Most modern AI systems use massive language models. These language models are trained on 6,000+ years of human text.
GPT-3 ate 8 billion pages, almost every book, and Wikipedia. It created an AI that can write sea shanties and solve coding problems.
Nothing new. I began beta testing GPT-3 in 2020, but the system's basics date back further.
Tools like GPT-3 are hidden in many apps. Many of the AI writing assistants on this platform are just wrappers around GPT-3.
Lots of online utilitarian text, like restaurant menu summaries or city guides, is written by AI systems like GPT-3. You've probably read GPT-3 without knowing it.
Accessibility
Why is ChatGPT so popular if the technology is old?
ChatGPT makes the technology accessible. Free to use, people can sign up and text with the chatbot daily. ChatGPT isn't revolutionary. It does it in a way normal people can access and be amazed by.
Accessibility isn't easy. OpenAI's Sam Altman tweeted that opening ChatGPT to the public increased computing costs.
Each chat costs "low-digit cents" to process. OpenAI probably spends several hundred thousand dollars a day to keep ChatGPT running, with no immediate business case.
Academic researchers and others who developed GPT-3 couldn't afford it. Without resources to make technology accessible, it can't be used.
Retrospective
This dynamic is old. In the history of science, a researcher with a breakthrough idea was often overshadowed by an entrepreneur or visionary who made it accessible to the public.
We think of Thomas Edison as the inventor of the lightbulb. But really, Vasilij Petrov, Thomas Wright, and Joseph Swan invented the lightbulb. Edison made technology visible and accessible by electrifying public buildings, building power plants, and wiring.
Edison probably lost a ton of money on stunts like building a power plant to light JP Morgan's home, the NYSE, and several newspaper headquarters.
People wanted electric lights once they saw their benefits. By making the technology accessible and visible, Edison unlocked a hugely profitable market.
Similar things are happening in AI. ChatGPT shows that developing breakthrough technology in the lab or on B2B servers won't change the culture.
AI must engage people's imaginations to become mainstream. Before the tech impacts the world, people must play with it and see its revolutionary power.
As the field evolves, companies that make the technology widely available, even at great cost, will succeed.
OpenAI's compute fees are eye-watering. Revolutions are costly.

Nick Babich
2 years ago
Is ChatGPT Capable of Generating a Complete Mobile App?
TL;DR: It'll be harder than you think.
Mobile app development is a complicated product design sector. You require broad expertise to create a mobile app. You must write Swift or Java code and consider mobile interactions.
When ChatGPT was released, many were amazed by its capabilities and wondered if it could replace designers and developers. This article will use ChatGPT to answer a specific query.
Can ChatGPT build an entire iOS app?
This post will use ChatGPT to construct an iOS meditation app. Video of the article is available.
App concepts for meditation
After deciding on an app, think about the user experience. What should the app offer?
Let's ask ChatGPT for the answer.
ChatGPT described a solid meditation app with various exercises. Use this list to plan product design. Our first product iteration will have few features. A simple, one-screen software will let users set the timeframe and play music during meditation.
Structure of information
Information architecture underpins product design. Our app's navigation mechanism should be founded on strong information architecture, so we need to identify our mobile's screens first.
ChatGPT can define our future app's information architecture since we already know it.
ChatGPT uses the more complicated product's structure. When adding features to future versions of our product, keep this information picture in mind.
Color palette
Meditation apps need colors. We want to employ relaxing colors in a meditation app because colors affect how we perceive items. ChatGPT can suggest product colors.
See the hues in person:
Neutral colors dominate the color scheme. Playing with color opacity makes this scheme useful.
Ambiance music
Meditation involves music. Well-chosen music calms the user.
Let ChatGPT make music for us.
ChatGPT can only generate text. It directs us to Spotify or YouTube to look for such stuff and makes precise recommendations.
Fonts
Fonts can impress app users. Round fonts are easier on the eyes and make a meditation app look friendlier.
ChatGPT can suggest app typefaces. I compare two font pairs when making a product. I'll ask ChatGPT for two font pairs.
See the hues in person:
Despite ChatGPT's convincing font pairing arguments, the output is unattractive. The initial combo (Open Sans + Playfair Display) doesn't seem to work well for a mediation app.
Content
Meditation requires the script. Find the correct words and read them calmly and soothingly to help listeners relax and focus on each region of their body to enhance the exercise's effect.
ChatGPT's offerings:
ChatGPT outputs code. My prompt's word script may cause it.
Timer
After fonts, colors, and content, construct functional pieces. Timer is our first functional piece. The meditation will be timed.
Let ChatGPT write Swift timer code (since were building an iOS app, we need to do it using Swift language).
ChatGPT supplied a timer class, initializer, and usage guidelines.
Apple Xcode requires a playground to test this code. Xcode will report issues after we paste the code to the playground.
Fixing them is simple. Just change Timer to another class name (Xcode shows errors because it thinks that we access the properties of the class we’ve created rather than the system class Timer; it happens because both classes have the same name Timer). I titled our class Timero and implemented the project. After this quick patch, ChatGPT's code works.
Can ChatGPT produce a complete app?
Since ChatGPT can help us construct app components, we may question if it can write a full app in one go.
Question ChatGPT:
ChatGPT supplied basic code and instructions. It's unclear if ChatGPT purposely limits output or if my prompt wasn't good enough, but the tool cannot produce an entire app from a single prompt.
However, we can contact ChatGPT for thorough Swift app construction instructions.
We can ask ChatGPT for step-by-step instructions now that we know what to do. Request a basic app layout from ChatGPT.
Copying this code to an Xcode project generates a functioning layout.
Takeaways
ChatGPT may provide step-by-step instructions on how to develop an app for a specific system, and individual steps can be utilized as prompts to ChatGPT. ChatGPT cannot generate the source code for the full program in one go.
The output that ChatGPT produces needs to be examined by a human. The majority of the time, you will need to polish or adjust ChatGPT's output, whether you develop a color scheme or a layout for the iOS app.
ChatGPT is unable to produce media material. Although ChatGPT cannot be used to produce images or sounds, it can assist you build prompts for programs like midjourney or Dalle-2 so that they can provide the appropriate images for you.
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Daniel Clery
3 years ago
Twisted device investigates fusion alternatives
German stellarator revamped to run longer, hotter, compete with tokamaks
Tokamaks have dominated the search for fusion energy for decades. Just as ITER, the world's largest and most expensive tokamak, nears completion in southern France, a smaller, twistier testbed will start up in Germany.
If the 16-meter-wide stellarator can match or outperform similar-size tokamaks, fusion experts may rethink their future. Stellarators can keep their superhot gases stable enough to fuse nuclei and produce energy. They can theoretically run forever, but tokamaks must pause to reset their magnet coils.
The €1 billion German machine, Wendelstein 7-X (W7-X), is already getting "tokamak-like performance" in short runs, claims plasma physicist David Gates, preventing particles and heat from escaping the superhot gas. If W7-X can go long, "it will be ahead," he says. "Stellarators excel" Eindhoven University of Technology theorist Josefine Proll says, "Stellarators are back in the game." A few of startup companies, including one that Gates is leaving Princeton Plasma Physics Laboratory, are developing their own stellarators.
W7-X has been running at the Max Planck Institute for Plasma Physics (IPP) in Greifswald, Germany, since 2015, albeit only at low power and for brief runs. W7-X's developers took it down and replaced all inner walls and fittings with water-cooled equivalents, allowing for longer, hotter runs. The team reported at a W7-X board meeting last week that the revised plasma vessel has no leaks. It's expected to restart later this month to show if it can get plasma to fusion-igniting conditions.
Wendelstein 7-X's water-cooled inner surface allows for longer runs.
HOSAN/IPP
Both stellarators and tokamaks create magnetic gas cages hot enough to melt metal. Microwaves or particle beams heat. Extreme temperatures create a plasma, a seething mix of separated nuclei and electrons, and cause the nuclei to fuse, releasing energy. A fusion power plant would use deuterium and tritium, which react quickly. Non-energy-generating research machines like W7-X avoid tritium and use hydrogen or deuterium instead.
Tokamaks and stellarators use electromagnetic coils to create plasma-confining magnetic fields. A greater field near the hole causes plasma to drift to the reactor's wall.
Tokamaks control drift by circulating plasma around a ring. Streaming creates a magnetic field that twists and stabilizes ionized plasma. Stellarators employ magnetic coils to twist, not plasma. Once plasma physicists got powerful enough supercomputers, they could optimize stellarator magnets to improve plasma confinement.
W7-X is the first large, optimized stellarator with 50 6- ton superconducting coils. Its construction began in the mid-1990s and cost roughly twice the €550 million originally budgeted.
The wait hasn't disappointed researchers. W7-X director Thomas Klinger: "The machine operated immediately." "It's a friendly machine." It did everything we asked." Tokamaks are prone to "instabilities" (plasma bulging or wobbling) or strong "disruptions," sometimes associated to halted plasma flow. IPP theorist Sophia Henneberg believes stellarators don't employ plasma current, which "removes an entire branch" of instabilities.
In early stellarators, the magnetic field geometry drove slower particles to follow banana-shaped orbits until they collided with other particles and leaked energy. Gates believes W7-X's ability to suppress this effect implies its optimization works.
W7-X loses heat through different forms of turbulence, which push particles toward the wall. Theorists have only lately mastered simulating turbulence. W7-X's forthcoming campaign will test simulations and turbulence-fighting techniques.
A stellarator can run constantly, unlike a tokamak, which pulses. W7-X has run 100 seconds—long by tokamak standards—at low power. The device's uncooled microwave and particle heating systems only produced 11.5 megawatts. The update doubles heating power. High temperature, high plasma density, and extensive runs will test stellarators' fusion power potential. Klinger wants to heat ions to 50 million degrees Celsius for 100 seconds. That would make W7-X "a world-class machine," he argues. The team will push for 30 minutes. "We'll move step-by-step," he says.
W7-X's success has inspired VCs to finance entrepreneurs creating commercial stellarators. Startups must simplify magnet production.
Princeton Stellarators, created by Gates and colleagues this year, has $3 million to build a prototype reactor without W7-X's twisted magnet coils. Instead, it will use a mosaic of 1000 HTS square coils on the plasma vessel's outside. By adjusting each coil's magnetic field, operators can change the applied field's form. Gates: "It moves coil complexity to the control system." The company intends to construct a reactor that can fuse cheap, abundant deuterium to produce neutrons for radioisotopes. If successful, the company will build a reactor.
Renaissance Fusion, situated in Grenoble, France, raised €16 million and wants to coat plasma vessel segments in HTS. Using a laser, engineers will burn off superconductor tracks to carve magnet coils. They want to build a meter-long test segment in 2 years and a full prototype by 2027.
Type One Energy in Madison, Wisconsin, won DOE money to bend HTS cables for stellarator magnets. The business carved twisting grooves in metal with computer-controlled etching equipment to coil cables. David Anderson of the University of Wisconsin, Madison, claims advanced manufacturing technology enables the stellarator.
Anderson said W7-X's next phase will boost stellarator work. “Half-hour discharges are steady-state,” he says. “This is a big deal.”

Vitalik
3 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3

Ari Joury, PhD
3 years ago
7 ways to turn into a major problem-solver
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:
Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?
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.
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!
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.
Google it. There is a purpose for the internet. Use it.
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.
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.
