## More on Personal Growth

Rajesh Gupta

1 year ago

## Why Is It So Difficult to Give Up Smoking?

I started smoking in 2002 at IIT BHU. Most of us thought it was enjoyable at first. I didn't realize the cost later.

In 2005, during my final semester, I lost my father. Suddenly, I felt more accountable for my mother and myself.

I quit before starting my first job in Bangalore. I didn't see any smoking friends in my hometown for 2 months before moving to Bangalore.

For the next 5-6 years, I had no regimen and smoked only when drinking.

Due to personal concerns, I started smoking again after my 2011 marriage. Now smoking was a constant guilty pleasure.

I smoked 3-4 cigarettes a day, but never in front of my family or on weekends. I used to excuse this with pride! First office ritual: smoking. Even with guilt, I couldn't stop this time because of personal concerns.

After 8-9 years, in mid 2019, a personal development program solved all my problems. I felt complete in myself. After this, I just needed one cigarette each day.

The hardest thing was leaving this final cigarette behind, even though I didn't want it.

James Clear's Atomic Habits was published last year. I'd only read 2-3 non-tech books before reading this one in August 2021. I knew everything but couldn't use it.

In April 2022, I realized the compounding effect of a bad habit thanks to my subconscious mind. 1 cigarette per day (excluding weekends) equals 240 = **24 packs per year**, which is a lot. No matter how much I did, it felt negative.

Then I applied the 2nd principle of this book, **identifying the trigger**. I tried to identify all the major triggers of smoking. *I found social drinking is one of them & If I am able to control it during that time, I can easily control it in other situations as well*. Going further whenever I drank, I was pre-determined to ignore the craving at any cost. Believe me, it was very hard initially but gradually this craving started fading away even with drinks.

I've been smoke-free for 3 months. Now I know a bad habit's effects. After realizing the power of habits, I'm developing other good habits which I ignored all my life.

NonConformist

1 year ago

## Before 6 AM, read these 6 quotations.

These quotes will change your perspective.

I try to reflect on these quotes daily. Reading it in the morning can affect your day, decisions, and priorities. Let's start.

# 1. Friedrich Nietzsche once said, "He who has a why to live for can bear almost any how."

What's your life goal?

80% of people don't know why they live or what they want to accomplish in life if you ask them randomly.

Even those with answers may not pursue their why. Without a purpose, life can be dull.

Your why can guide you through difficult times.

Create a life goal. Growing may change your goal. Having a purpose in life prevents feeling lost.

# 2. Seneca said, "He who fears death will never do anything fit for a man in life."

FAILURE STINKS Yes.

This quote is great if you're afraid to try because of failure. What if I'm not made for it? What will they think if I fail?

This wastes most of our lives. Many people prefer not failing over trying something with a better chance of success, according to studies.

Failure stinks in the short term, but it can transform our lives over time.

# 3. Two men peered through the bars of their cell windows; one saw mud, the other saw stars. — Dale Carnegie

It’s not what you look at that matters; it’s what you see.

The glass-full-or-empty meme is everywhere. It's hard to be positive when facing adversity.

This is a skill. Positive thinking can change our future.

We should stop complaining about our life and how easy success is for others.

Seductive pessimism. Realize this and start from first principles.

# 4. “**Smart people learn from everything and everyone, average people from their experiences, and stupid people already have all the answers.”** — Socrates.

Knowing we're ignorant can be helpful.

Every person and situation teaches you something. You can learn from others' experiences so you don't have to. Analyzing your and others' actions and applying what you learn can be beneficial.

Reading (especially non-fiction or biographies) is a good use of time. Walter Issacson wrote Benjamin Franklin's biography. Ben Franklin's early mistakes and successes helped me in some ways.

Knowing everything leads to disaster. Every incident offers lessons.

# 5. “**We must all suffer one of two things: the pain of discipline or the pain of regret or disappointment.**“ — James Rohn

My favorite Jim Rohn quote.

Exercise hurts. Healthy eating can be painful. But they're needed to get in shape. Avoiding pain can ruin our lives.

Always choose progress over hopelessness. Myth: overnight success Everyone who has mastered a craft knows that mastery comes from overcoming laziness.

Turn off your inner critic and start working. Try Can't Hurt Me by David Goggins.

# 6. “**A champion is defined not by their wins, but by how they can recover when they fail.**“ — Serena Williams

Have you heard of **Traf-o-Data**?

Gates and Allen founded Traf-O-Data. After some success, it failed. Traf-o-Data's failure led to Microsoft.

Allen said Traf-O-Data's setback was important for Microsoft's first product a few years later. Traf-O-Data was a business failure, but it helped them understand microprocessors, he wrote in 2017.

“The obstacle in the path becomes the path. Never forget, within every obstacle is an opportunity to improve our condition.” — Ryan Holiday.

# Bonus Quotes

More helpful quotes:

“Those who cannot change their minds cannot change anything.” — George Bernard Shaw.

“Do something every day that you don’t want to do; this is the golden rule for acquiring the habit of doing your duty without pain.” — Mark Twain.

“Never give up on a dream just because of the time it will take to accomplish it. The time will pass anyway.” — Earl Nightingale.

“A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.” — George Bernard Shaw.

“We don’t stop playing because we grow old; we grow old because we stop playing.” — George Bernard Shaw.

# Conclusion

Words are powerful. Utilize it. Reading these inspirational quotes will help you.

Zuzanna Sieja

1 year ago

## In 2022, each data scientist needs to read these 11 books.

Non-technical talents can benefit data scientists in addition to statistics and programming.

As our article 5 Most In-Demand Skills for Data Scientists shows, being business-minded is useful. How can you get such a diverse skill set? We've compiled a list of helpful resources.

Data science, data analysis, programming, and business are covered. Even a few of these books will make you a better data scientist.

Ready? Let’s dive in.

# Best books for data scientists

# 1. The Black Swan

**Author:** Nassim Taleb

First, a less obvious title. Nassim Nicholas Taleb's seminal series examines uncertainty, probability, risk, and decision-making.

Three characteristics define a black swan event:

It is erratic.

It has a significant impact.

Many times, people try to come up with an explanation that makes it seem more predictable than it actually was.

People formerly believed all swans were white because they'd never seen otherwise. A black swan in Australia shattered their belief.

Taleb uses this incident to illustrate how human thinking mistakes affect decision-making. The book teaches readers to be aware of unpredictability in the ever-changing IT business.

Try multiple tactics and models because you may find the answer.

# 2. High Output Management

**Author:** Andrew Grove

Intel's former chairman and CEO provides his insights on developing a global firm in this business book. We think Grove would choose “management” to describe the talent needed to start and run a business.

That's a skill for CEOs, techies, and data scientists. Grove writes on developing productive teams, motivation, real-life business scenarios, and revolutionizing work.

Five lessons:

Every action is a procedure.

Meetings are a medium of work

Manage short-term goals in accordance with long-term strategies.

Mission-oriented teams accelerate while functional teams increase leverage.

Utilize performance evaluations to enhance output.

So — if the above captures your imagination, it’s well worth getting stuck in.

# 3. The Hard Thing About Hard Things: Building a Business When There Are No Easy Answers

**Author:** Ben Horowitz

Few realize how difficult it is to run a business, even though many see it as a tremendous opportunity.

Business schools don't teach managers how to handle the toughest difficulties; they're usually on their own. So Ben Horowitz wrote this book.

It gives tips on creating and maintaining a new firm and analyzes the hurdles CEOs face.

Find suggestions on:

create software

Run a business.

Promote a product

Obtain resources

Smart investment

oversee daily operations

This book will help you cope with tough times.

# 4. Obviously Awesome: How to Nail Product Positioning

**Author: **April Dunford

Your job as a data scientist is a product. You should be able to sell what you do to clients. Even if your product is great, you must convince them.

How to? April Dunford's advice: Her book explains how to connect with customers by making your offering seem like a secret sauce.

You'll learn:

Select the ideal market for your products.

Connect an audience to the value of your goods right away.

Take use of three positioning philosophies.

Utilize market trends to aid purchasers

# 5. The Mom test

**Author: **Rob Fitzpatrick

The Mom Test improves communication. Client conversations are rarely predictable. The book emphasizes one of the most important communication rules: enquire about specific prior behaviors.

Both ways work. If a client has suggestions or demands, listen carefully and ensure everyone understands. The book is packed with client-speaking tips.

# 6. Introduction to Machine Learning with Python: A Guide for Data Scientists

**Authors:** Andreas C. Müller, Sarah Guido

Now, technical documents.

This book is for Python-savvy data scientists who wish to learn machine learning. Authors explain how to use algorithms instead of math theory.

Their technique is ideal for developers who wish to study machine learning basics and use cases. Sci-kit-learn, NumPy, SciPy, pandas, and Jupyter Notebook are covered beyond Python.

If you know machine learning or artificial neural networks, skip this.

# 7. Python Data Science Handbook: Essential Tools for Working with Data

**Author:** Jake VanderPlas

Data work isn't easy. Data manipulation, transformation, cleansing, and visualization must be exact.

Python is a popular tool. The Python Data Science Handbook explains everything. The book describes how to utilize Pandas, Numpy, Matplotlib, Scikit-Learn, and Jupyter for beginners.

The only thing missing is a way to apply your learnings.

# 8. Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython

**Author:** Wes McKinney

The author leads you through manipulating, processing, cleaning, and analyzing Python datasets using NumPy, Pandas, and IPython.

The book's realistic case studies make it a great resource for Python or scientific computing beginners. Once accomplished, you'll uncover online analytics, finance, social science, and economics solutions.

# 9. Data Science from Scratch

**Author:** Joel Grus

Here's a title for data scientists with Python, stats, maths, and algebra skills (alongside a grasp of algorithms and machine learning). You'll learn data science's essential libraries, frameworks, modules, and toolkits.

The author works through all the key principles, providing you with the practical abilities to develop simple code. The book is appropriate for intermediate programmers interested in data science and machine learning.

Not that prior knowledge is required. The writing style matches all experience levels, but understanding will help you absorb more.

# 10. Machine Learning Yearning

**Author:** Andrew Ng

Andrew Ng is a machine learning expert. Co-founded and teaches at Stanford. This free book shows you how to structure an ML project, including recognizing mistakes and building in complex contexts.

The book delivers knowledge and teaches how to apply it, so you'll know how to:

Determine the optimal course of action for your ML project.

Create software that is more effective than people.

Recognize when to use end-to-end, transfer, and multi-task learning, and how to do so.

Identifying machine learning system flaws

Ng writes easy-to-read books. No rigorous math theory; just a terrific approach to understanding how to make technical machine learning decisions.

# 11. Deep Learning with PyTorch Step-by-Step

**Author:** Daniel Voigt Godoy

The last title is also the most recent. The book was revised on 23 January 2022 to discuss Deep Learning and PyTorch, a Python coding tool.

It comprises four parts:

Fundamentals (gradient descent, training linear and logistic regressions in PyTorch)

Machine Learning (deeper models and activation functions, convolutions, transfer learning, initialization schemes)

Sequences (RNN, GRU, LSTM, seq2seq models, attention, self-attention, transformers)

Automatic Language Recognition (tokenization, embeddings, contextual word embeddings, ELMo, BERT, GPT-2)

We admire the book's readability. The author avoids difficult mathematical concepts, making the material feel like a conversation.

# Is every data scientist a humanist?

Even as a technological professional, you can't escape human interaction, especially with clients.

We hope these books will help you develop interpersonal skills.

## You might also like

Farhan Ali Khan

1 year ago

## Introduction to Zero-Knowledge Proofs: The Art of Proving Without Revealing

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).

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

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

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:

Alex walks into the cave.

Alex follows a random route.

Jack walks into the cave.

Alex is asked to follow a random route by Jack.

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

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

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

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:

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

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.

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

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:

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

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.

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:

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

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

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

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.

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:

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.

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.

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:

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

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.

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

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.

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:

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.

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.

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:

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.

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.

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.

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.

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:

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.

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.

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.

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.

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.

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:

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.

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.

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.

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.

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.

Vitalik

2 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

Onchain Wizard

2 years ago

## Three Arrows Capital & Celsius Updates

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

## 3AC's liquidation documents:

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

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

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

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

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

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

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

Genesis demanded $355mm in further collateral in June.

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

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

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

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

## Celsius:

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

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

## Conclusion

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

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

*To see the full article, click **here**.*