Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

Better technology and lower launch costs revive science-fiction tech.

Airbus engineers showed off sustainable energy's future in Munich last month. They captured sunlight with solar panels, turned it into microwaves, and beamed it into an airplane hangar, where it lighted a city model. The test delivered 2 kW across 36 meters, but it posed a serious question: Should we send enormous satellites to capture solar energy in space? In orbit, free of clouds and nighttime, they could create power 24/7 and send it to Earth.

Airbus engineer Jean-Dominique Coste calls it an engineering problem. “But it’s never been done at [large] scale.”

Proponents of space solar power say the demand for green energy, cheaper space access, and improved technology might change that. Once someone invests commercially, it will grow. Former NASA researcher John Mankins says it might be a trillion-dollar industry.

Myriad uncertainties remain, including whether beaming gigawatts of power to Earth can be done efficiently and without burning birds or people. Concept papers are being replaced with ground and space testing. The European Space Agency (ESA), which supported the Munich demo, will propose ground tests to member nations next month. The U.K. government offered £6 million to evaluate innovations this year. Chinese, Japanese, South Korean, and U.S. agencies are working. NASA policy analyst Nikolai Joseph, author of an upcoming assessment, thinks the conversation's tone has altered. What formerly appeared unattainable may now be a matter of "bringing it all together"

NASA studied space solar power during the mid-1970s fuel crunch. A projected space demonstration trip using 1970s technology would have cost $1 trillion. According to Mankins, the idea is taboo in the agency.

Space and solar power technology have evolved. Photovoltaic (PV) solar cell efficiency has increased 25% over the past decade, Jones claims. Telecoms use microwave transmitters and receivers. Robots designed to repair and refuel spacecraft might create solar panels.

Falling launch costs have boosted the idea. A solar power satellite large enough to replace a nuclear or coal plant would require hundreds of launches. ESA scientist Sanjay Vijendran: "It would require a massive construction complex in orbit."

SpaceX has made the idea more plausible. A SpaceX Falcon 9 rocket costs $2600 per kilogram, less than 5% of what the Space Shuttle did, and the company promised $10 per kilogram for its giant Starship, slated to launch this year. Jones: "It changes the equation." "Economics rules"

Mass production reduces space hardware costs. Satellites are one-offs made with pricey space-rated parts. Mars rover Perseverance cost $2 million per kilogram. SpaceX's Starlink satellites cost less than $1000 per kilogram. This strategy may work for massive space buildings consisting of many identical low-cost components, Mankins has long contended. Low-cost launches and "hypermodularity" make space solar power economical, he claims.

Better engineering can improve economics. Coste says Airbus's Munich trial was 5% efficient, comparing solar input to electricity production. When the Sun shines, ground-based solar arrays perform better. Studies show space solar might compete with existing energy sources on price if it reaches 20% efficiency.

Lighter parts reduce costs. "Sandwich panels" with PV cells on one side, electronics in the middle, and a microwave transmitter on the other could help. Thousands of them build a solar satellite without heavy wiring to move power. In 2020, a team from the U.S. Naval Research Laboratory (NRL) flew on the Air Force's X-37B space plane.

NRL project head Paul Jaffe said the satellite is still providing data. The panel converts solar power into microwaves at 8% efficiency, but not to Earth. The Air Force expects to test a beaming sandwich panel next year. MIT will launch its prototype panel with SpaceX in December.

As a satellite orbits, the PV side of sandwich panels sometimes faces away from the Sun since the microwave side must always face Earth. To maintain 24-hour power, a satellite needs mirrors to keep that side illuminated and focus light on the PV. In a 2012 NASA study by Mankins, a bowl-shaped device with thousands of thin-film mirrors focuses light onto the PV array.

International Electric Company's Ian Cash has a new strategy. His proposed satellite uses enormous, fixed mirrors to redirect light onto a PV and microwave array while the structure spins (see graphic, above). 1 billion minuscule perpendicular antennas act as a "phased array" to electronically guide the beam toward Earth, regardless of the satellite's orientation. This design, argues Cash, is "the most competitive economically"

If a space-based power plant ever flies, its power must be delivered securely and efficiently. Jaffe's team at NRL just beamed 1.6 kW over 1 km, and teams in Japan, China, and South Korea have comparable attempts. Transmitters and receivers lose half their input power. Vijendran says space solar beaming needs 75% efficiency, "preferably 90%."

Beaming gigawatts through the atmosphere demands testing. Most designs aim to produce a beam kilometers wide so every ship, plane, human, or bird that strays into it only receives a tiny—hopefully harmless—portion of the 2-gigawatt transmission. Receiving antennas are cheap to build but require a lot of land, adds Jones. You could grow crops under them or place them offshore.

Europe's public agencies currently prioritize space solar power. Jones: "There's a devotion you don't see in the U.S." ESA commissioned two solar cost/benefit studies last year. Vijendran claims it might match ground-based renewables' cost. Even at a higher price, equivalent to nuclear, its 24/7 availability would make it competitive.

ESA will urge member states in November to fund a technical assessment. If the news is good, the agency will plan for 2025. With €15 billion to €20 billion, ESA may launch a megawatt-scale demonstration facility by 2030 and a gigawatt-scale facility by 2040. "Moonshot"

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.

1. Write down the things that are causing you anxiety at the moment.

2. Describe a situation in which you felt anxious and how you coped with it.

3. Reflect on how your thoughts and beliefs contribute to your anxiety.

4. Write a letter to your anxiety, expressing your feelings and concerns

5. Imagine yourself in a calm and peaceful place, and describe it in detail.

6. (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:

1. 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.

2. Show the timeline of significant events in the history of AI, and discuss the key milestones and developments in the field.

3. Show examples of AI technologies and applications, and explain how they are used in various industries and fields.

4. 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.

DATA MINING WITH SUPERALGORES

Old pots produce the best soup.

Science has always inspired indicator design. From physics to signal processing, many indicators use concepts from mechanical engineering, electronics, and probability. In Superalgos' Data Mining section, we've explored using thermodynamics and information theory to construct indicators and using statistical and probabilistic techniques like reduced normal law to take advantage of low probability events.

An asset's price is like a mechanical object revolving around its moving average. Using this approach, we could design an indicator using the oscillator's Total Energy. An oscillator's energy is finite and constant. Since we don't expect the price to follow the harmonic oscillator, this energy should deviate from the perfect situation, and the maximum of divergence may provide us valuable information on the price's moving average.

Definition of the Harmonic Oscillator in Few Words

Sinusoidal function describes a harmonic oscillator. The time-constant energy equation for a harmonic oscillator is:

With

Time saves energy.

In a mechanical harmonic oscillator, total energy equals kinetic energy plus potential energy. The formula for energy is the same for every kind of harmonic oscillator; only the terms of total energy must be adapted to fit the relevant units. Each oscillator has a velocity component (kinetic energy) and a position to equilibrium component (potential energy).

The Price Oscillator and the Energy Formula

Considering the harmonic oscillator definition, we must specify kinetic and potential components for our price oscillator. We define oscillator velocity as the rate of change and equilibrium position as the price's distance from its moving average.

Price kinetic energy:

It's like:

With

and

L is the number of periods for the rate of change calculation and P for the close price EMA calculation.

Total price oscillator energy =

Given that an asset's price can theoretically vary at a limitless speed and be endlessly far from its moving average, we don't expect this formula's outcome to be constrained. We'll normalize it using Z-Score for convenience of usage and readability, which also allows probabilistic interpretation.

Over 20 periods, we'll calculate E's moving average and standard deviation.

We calculated Z on BTC/USDT with L = 10 and P = 21 using Knime Analytics.

The graph is detrended. We added two horizontal lines at +/- 1.6 to construct a 94.5% probability zone based on reduced normal law tables. Price cycles to its moving average oscillate clearly. Red and green arrows illustrate where the oscillator crosses the top and lower limits, corresponding to the maximum/minimum price oscillation. Since the results seem noisy, we may apply a non-lagging low-pass or multipole filter like Butterworth or Laguerre filters and employ dynamic bands at a multiple of Z's standard deviation instead of fixed levels.

Kinetic Detrender Implementation in Superalgos

The Superalgos Kinetic detrender features fixed upper and lower levels and dynamic volatility bands.

The code is pretty basic and does not require a huge amount of code lines.

It starts with the standard definitions of the candle pointer and the constant declaration :

let candle = record.current
let len = 10
let P = 21
let T = 20
let up = 1.6
let low = 1.6

Upper and lower dynamic volatility band constants are up and low.

We proceed to the initialization of the previous value for EMA :

if (variable.prevEMA === undefined) {
    variable.prevEMA = candle.close
}

And the calculation of EMA with a function (it is worth noticing the function is declared at the end of the code snippet in Superalgos) :

variable.ema = calculateEMA(P, candle.close, variable.prevEMA)
//EMA calculation
function calculateEMA(periods, price, previousEMA) {
    let k = 2 / (periods + 1)
    return price * k + previousEMA * (1 - k)
}

The rate of change is calculated by first storing the right amount of close price values and proceeding to the calculation by dividing the current close price by the first member of the close price array:

variable.allClose.push(candle.close)
if (variable.allClose.length > len) {
    variable.allClose.splice(0, 1)
}
if (variable.allClose.length === len) {
    variable.roc = candle.close / variable.allClose[0]
} else {
    variable.roc = 1
}

Finally, we get energy with a single line:

variable.E = 1 / 2 * len * variable.roc + 1 / 2 * P * candle.close / variable.ema

The Z calculation reuses code from Z-Normalization-based indicators:

variable.allE.push(variable.E)
if (variable.allE.length > T) {
    variable.allE.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allE.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allE[i]
    }
    variable.MA = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allE[i] - variable.MA, 2)
    }
    variable.sigma = Math.sqrt(variable.SQ / T)
variable.Z = (variable.E - variable.MA) / variable.sigma
} else {
    variable.Z = 0
}
variable.allZ.push(variable.Z)
if (variable.allZ.length > T) {
    variable.allZ.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allZ.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allZ[i]
    }
    variable.MAZ = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allZ[i] - variable.MAZ, 2)
    }
    variable.sigZ = Math.sqrt(variable.SQ / T)
} else {
    variable.MAZ = variable.Z
    variable.sigZ = variable.MAZ * 0.02
}
variable.upper = variable.MAZ + up * variable.sigZ
variable.lower = variable.MAZ - low * variable.sigZ

We also update the EMA value.

variable.prevEMA = variable.EMA

Conclusion

We showed how to build a detrended oscillator using simple harmonic oscillator theory. Kinetic detrender's main line oscillates between 2 fixed levels framing 95% of the values and 2 dynamic levels, leading to auto-adaptive mean reversion zones.

Superalgos' Normalized Momentum data mine has the Kinetic detrender indication.

All the material here can be reused and integrated freely by linking to this article and Superalgos.

This post is informative and not financial advice. Seek expert counsel before trading. Risk using this material.