Integrity
Write
Loading...
Vitalik

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

(Edited)

Hackernoon

Hackernoon

3 years ago


👏 Awesome post! When is part 3 coming?

Trent Lapinski

Trent Lapinski

3 years ago

Very complex topic, great explanation

More on Web3 & Crypto

Jayden Levitt

Jayden Levitt

2 years ago

The country of El Salvador's Bitcoin-obsessed president lost $61.6 million.

It’s only a loss if you sell, right?

Created by Author — Using Toonme

Nayib Bukele proclaimed himself “the world’s coolest dictator”.

His jokes aren't clear.

El Salvador's 43rd president self-proclaimed “CEO of El Salvador” couldn't be less presidential.

His thin jeans, aviator sunglasses, and baseball caps like a cartel lord.

He's popular, though.

Bukele won 53% of the vote by fighting violent crime and opposition party corruption.

El Salvador's 6.4 million inhabitants are riding the cryptocurrency volatility wave.

They were powerless.

Their autocratic leader, a former Yamaha Motors salesperson and Bitcoin believer, wants to help 70% unbanked locals.

He intended to give the citizens a way to save money and cut the country's $200 million remittance cost.

Transfer and deposit costs.

This makes logical sense when the president’s theatrics don’t blind you.

El Salvador's Bukele revealed plans to make bitcoin legal tender.

Remittances total $5.9 billion (23%) of the country's expenses.

Anything that reduces costs could boost the economy.

The country’s unbanked population is staggering. Here’s the data by % of people who either have a bank account (Blue) or a mobile money account (Black).

Source — statista.com

According to Bukele, 46% of the population has downloaded the Chivo Bitcoin Wallet.

In 2021, 36% of El Salvadorans had bank accounts.


Large rural countries like Kenya seem to have resolved their unbanked dilemma.

An economy surfaced where village locals would sell, trade and store network minutes and data as a store of value.

Kenyan phone networks realized unbanked people needed a safe way to accumulate wealth and have an emergency fund.

96% of Kenyans utilize M-PESA, which doesn't require a bank account.

The software involves human agents who hang out with cash and a phone.

These people are like ATMs.

You offer them cash to deposit money in your mobile money account or withdraw cash.

In a country with a faulty banking system, cash availability and a safe place to deposit it are important.

William Jack and Tavneet Suri found that M-PESA brought 194,000 Kenyan households out of poverty by making transactions cheaper and creating a safe store of value.

2016 Science paper

Mobile money, a service that allows monetary value to be stored on a mobile phone and sent to other users via text messages, has been adopted by most Kenyan households. We estimate that access to the Kenyan mobile money system M-PESA increased per capita consumption levels and lifted 194,000 households, or 2% of Kenyan households, out of poverty.

The impacts, which are more pronounced for female-headed households, appear to be driven by changes in financial behaviour — in particular, increased financial resilience and saving. Mobile money has therefore increased the efficiency of the allocation of consumption over time while allowing a more efficient allocation of labour, resulting in a meaningful reduction of poverty in Kenya.


Currently, El Salvador has 2,301 Bitcoin.

At publication, it's worth $44 million. That remains 41% of Bukele's original $105.6 million.

Unknown if the country has sold Bitcoin, but Bukeles keeps purchasing the dip.

It's still falling.

Source — Nayib Bukele — Twitter

This might be a fantastic move for the impoverished country over the next five years, if they can live economically till Bitcoin's price recovers.

The evidence demonstrates that a store of value pulls individuals out of poverty, but others say Bitcoin is premature.

You may regard it as an aggressive endeavor to front run the next wave of adoption, offering El Salvador a financial upside.

Percy Bolmér

Percy Bolmér

2 years ago

Ethereum No Longer Consumes A Medium-Sized Country's Electricity To Run

The Merge cut Ethereum's energy use by 99.5%.

Image by Percy Bolmér. Gopher by Takuya Ueda, Original Go Gopher by Renée French (CC BY 3.0)

The Crypto community celebrated on September 15, 2022. This day, Ethereum Merged. The entire blockchain successfully merged with the Beacon chain, and it was so smooth you barely noticed.

Many have waited, dreaded, and longed for this day.

Some investors feared the network would break down, while others envisioned a seamless merging.

Speculators predict a successful Merge will lead investors to Ethereum. This could boost Ethereum's popularity.

What Has Changed Since The Merge

The merging transitions Ethereum mainnet from PoW to PoS.

PoW sends a mathematical riddle to computers worldwide (miners). First miner to solve puzzle updates blockchain and is rewarded.

The puzzles sent are power-intensive to solve, so mining requires a lot of electricity. It's sent to every miner competing to solve it, requiring duplicate computation.

PoS allows investors to stake their coins to validate a new transaction. Instead of validating a whole block, you validate a transaction and get the fees.

You can validate instead of mine. A validator stakes 32 Ethereum. After staking, the validator can validate future blocks.

Once a validator validates a block, it's sent to a randomly selected group of other validators. This group verifies that a validator is not malicious and doesn't validate fake blocks.

This way, only one computer needs to solve or validate the transaction, instead of all miners. The validated block must be approved by a small group of validators, causing duplicate computation.

PoS is more secure because validating fake blocks results in slashing. You lose your bet tokens. If a validator signs a bad block or double-signs conflicting blocks, their ETH is burned.

Theoretically, Ethereum has one block every 12 seconds, so a validator forging a block risks burning 1 Ethereum for 12 seconds of transactions. This makes mistakes expensive and risky.

What Impact Does This Have On Energy Use?

Cryptocurrency is a natural calamity, sucking electricity and eating away at the earth one transaction at a time.

Many don't know the environmental impact of cryptocurrencies, yet it's tremendous.

A single Ethereum transaction used to use 200 kWh and leave a large carbon imprint. This update reduces global energy use by 0.2%.

Energy consumption PER transaction for Ethereum post-merge. Image from Digiconomist

Ethereum will submit a challenge to one validator, and that validator will forward it to randomly selected other validators who accept it.

This reduces the needed computing power.

They expect a 99.5% reduction, therefore a single transaction should cost 1 kWh.

Carbon footprint is 0.58 kgCO2, or 1,235 VISA transactions.

This is a big Ethereum blockchain update.

I love cryptocurrency and Mother Earth.

Langston Thomas

3 years ago

A Simple Guide to NFT Blockchains

Ethereum's blockchain rules NFTs. Many consider it the one-stop shop for NFTs, and it's become the most talked-about and trafficked blockchain in existence.

Other blockchains are becoming popular in NFTs. Crypto-artists and NFT enthusiasts have sought new places to mint and trade NFTs due to Ethereum's high transaction costs and environmental impact.

When choosing a blockchain to mint on, there are several factors to consider. Size, creator costs, consumer spending habits, security, and community input are important. We've created a high-level summary of blockchains for NFTs to help clarify the fast-paced world of web3 tech.

Ethereum

Ethereum currently has the most NFTs. It's decentralized and provides financial and legal services without intermediaries. It houses popular NFT marketplaces (OpenSea), projects (CryptoPunks and the Bored Ape Yacht Club), and artists (Pak and Beeple).

It's also expensive and energy-intensive. This is because Ethereum works using a Proof-of-Work (PoW) mechanism. PoW requires computers to solve puzzles to add blocks and transactions to the blockchain. Solving these puzzles requires a lot of computer power, resulting in astronomical energy loss.

You should consider this blockchain first due to its popularity, security, decentralization, and ease of use.

Solana

Solana is a fast programmable blockchain. Its proof-of-history and proof-of-stake (PoS) consensus mechanisms eliminate complex puzzles. Reduced validation times and fees result.

PoS users stake their cryptocurrency to become a block validator. Validators get SOL. This encourages and rewards users to become stakers. PoH works with PoS to cryptographically verify time between events. Solana blockchain ensures transactions are in order and found by the correct leader (validator).

Solana's PoS and PoH mechanisms keep transaction fees and times low. Solana isn't as popular as Ethereum, so there are fewer NFT marketplaces and blockchain traders.

Tezos

Tezos is a greener blockchain. Tezos rose in 2021. Hic et Nunc was hailed as an economic alternative to Ethereum-centric marketplaces until Nov. 14, 2021.

Similar to Solana, Tezos uses a PoS consensus mechanism and only a PoS mechanism to reduce computational work. This blockchain uses two million times less energy than Ethereum. It's cheaper than Ethereum (but does cost more than Solana).

Tezos is a good place to start minting NFTs in bulk. Objkt is the largest Tezos marketplace.

Flow

Flow is a high-performance blockchain for NFTs, games, and decentralized apps (dApps). Flow is built with scalability in mind, so billions of people could interact with NFTs on the blockchain.

Flow became the NBA's blockchain partner in 2019. Flow, a product of Dapper labs (the team behind CryptoKitties), launched and hosts NBA Top Shot, making the blockchain integral to the popularity of non-fungible tokens.

Flow uses PoS to verify transactions, like Tezos. Developers are working on a model to handle 10,000 transactions per second on the blockchain. Low transaction fees.

Flow NFTs are tradeable on Blocktobay, OpenSea, Rarible, Foundation, and other platforms. NBA, NFL, UFC, and others have launched NFT marketplaces on Flow. Flow isn't as popular as Ethereum, resulting in fewer NFT marketplaces and blockchain traders.

Asset Exchange (WAX)

WAX is king of virtual collectibles. WAX is popular for digitalized versions of legacy collectibles like trading cards, figurines, memorabilia, etc.

Wax uses a PoS mechanism, but also creates carbon offset NFTs and partners with Climate Care. Like Flow, WAX transaction fees are low, and network fees are redistributed to the WAX community as an incentive to collectors.

WAX marketplaces host Topps, NASCAR, Hot Wheels, and cult classic film franchises like Godzilla, The Princess Bride, and Spiderman.

Binance Smart Chain

BSC is another good option for balancing fees and performance. High-speed transactions and low fees hurt decentralization. BSC is most centralized.

Binance Smart Chain uses Proof of Staked Authority (PoSA) to support a short block time and low fees. The 21 validators needed to run the exchange switch every 24 hours. 11 of the 21 validators are directly connected to the Binance Crypto Exchange, according to reports.

While many in the crypto and NFT ecosystems dislike centralization, the BSC NFT market picked up speed in 2021. OpenBiSea, AirNFTs, JuggerWorld, and others are gaining popularity despite not having as robust an ecosystem as Ethereum.

You might also like

Sofien Kaabar, CFA

Sofien Kaabar, CFA

2 years ago

How to Make a Trading Heatmap

Python Heatmap Technical Indicator

Heatmaps provide an instant overview. They can be used with correlations or to predict reactions or confirm the trend in trading. This article covers RSI heatmap creation.

The Market System

Market regime:

  • Bullish trend: The market tends to make higher highs, which indicates that the overall trend is upward.

  • Sideways: The market tends to fluctuate while staying within predetermined zones.

  • Bearish trend: The market has the propensity to make lower lows, indicating that the overall trend is downward.

Most tools detect the trend, but we cannot predict the next state. The best way to solve this problem is to assume the current state will continue and trade any reactions, preferably in the trend.

If the EURUSD is above its moving average and making higher highs, a trend-following strategy would be to wait for dips before buying and assuming the bullish trend will continue.

Indicator of Relative Strength

J. Welles Wilder Jr. introduced the RSI, a popular and versatile technical indicator. Used as a contrarian indicator to exploit extreme reactions. Calculating the default RSI usually involves these steps:

  • Determine the difference between the closing prices from the prior ones.

  • Distinguish between the positive and negative net changes.

  • Create a smoothed moving average for both the absolute values of the positive net changes and the negative net changes.

  • Take the difference between the smoothed positive and negative changes. The Relative Strength RS will be the name we use to describe this calculation.

  • To obtain the RSI, use the normalization formula shown below for each time step.

GBPUSD in the first panel with the 13-period RSI in the second panel.

The 13-period RSI and black GBPUSD hourly values are shown above. RSI bounces near 25 and pauses around 75. Python requires a four-column OHLC array for RSI coding.

import numpy as np
def add_column(data, times):
    
    for i in range(1, times + 1):
    
        new = np.zeros((len(data), 1), dtype = float)
        
        data = np.append(data, new, axis = 1)
    return data
def delete_column(data, index, times):
    
    for i in range(1, times + 1):
    
        data = np.delete(data, index, axis = 1)
    return data
def delete_row(data, number):
    
    data = data[number:, ]
    
    return data
def ma(data, lookback, close, position): 
    
    data = add_column(data, 1)
    
    for i in range(len(data)):
           
            try:
                
                data[i, position] = (data[i - lookback + 1:i + 1, close].mean())
            
            except IndexError:
                
                pass
            
    data = delete_row(data, lookback)
    
    return data
def smoothed_ma(data, alpha, lookback, close, position):
    
    lookback = (2 * lookback) - 1
    
    alpha = alpha / (lookback + 1.0)
    
    beta  = 1 - alpha
    
    data = ma(data, lookback, close, position)
    data[lookback + 1, position] = (data[lookback + 1, close] * alpha) + (data[lookback, position] * beta)
    for i in range(lookback + 2, len(data)):
        
            try:
                
                data[i, position] = (data[i, close] * alpha) + (data[i - 1, position] * beta)
        
            except IndexError:
                
                pass
            
    return data
def rsi(data, lookback, close, position):
    
    data = add_column(data, 5)
    
    for i in range(len(data)):
        
        data[i, position] = data[i, close] - data[i - 1, close]
     
    for i in range(len(data)):
        
        if data[i, position] > 0:
            
            data[i, position + 1] = data[i, position]
            
        elif data[i, position] < 0:
            
            data[i, position + 2] = abs(data[i, position])
            
    data = smoothed_ma(data, 2, lookback, position + 1, position + 3)
    data = smoothed_ma(data, 2, lookback, position + 2, position + 4)
    data[:, position + 5] = data[:, position + 3] / data[:, position + 4]
    
    data[:, position + 6] = (100 - (100 / (1 + data[:, position + 5])))
    data = delete_column(data, position, 6)
    data = delete_row(data, lookback)
    return data

Make sure to focus on the concepts and not the code. You can find the codes of most of my strategies in my books. The most important thing is to comprehend the techniques and strategies.

My weekly market sentiment report uses complex and simple models to understand the current positioning and predict the future direction of several major markets. Check out the report here:

Using the Heatmap to Find the Trend

RSI trend detection is easy but useless. Bullish and bearish regimes are in effect when the RSI is above or below 50, respectively. Tracing a vertical colored line creates the conditions below. How:

  • When the RSI is higher than 50, a green vertical line is drawn.

  • When the RSI is lower than 50, a red vertical line is drawn.

Zooming out yields a basic heatmap, as shown below.

100-period RSI heatmap.

Plot code:

def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)  
        if sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

100-period RSI heatmap.

Call RSI on your OHLC array's fifth column. 4. Adjusting lookback parameters reduces lag and false signals. Other indicators and conditions are possible.

Another suggestion is to develop an RSI Heatmap for Extreme Conditions.

Contrarian indicator RSI. The following rules apply:

  • Whenever the RSI is approaching the upper values, the color approaches red.

  • The color tends toward green whenever the RSI is getting close to the lower values.

Zooming out yields a basic heatmap, as shown below.

13-period RSI heatmap.

Plot code:

import matplotlib.pyplot as plt
def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
        if sample[i, second_panel] > 80 and sample[i, second_panel] < 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'darkred', linewidth = 1.5)  
        if sample[i, second_panel] > 70 and sample[i, second_panel] < 80:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'maroon', linewidth = 1.5)  
        if sample[i, second_panel] > 60 and sample[i, second_panel] < 70:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'firebrick', linewidth = 1.5) 
        if sample[i, second_panel] > 50 and sample[i, second_panel] < 60:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 40 and sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 30 and sample[i, second_panel] < 40:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'lightgreen', linewidth = 1.5)
        if sample[i, second_panel] > 20 and sample[i, second_panel] < 30:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'limegreen', linewidth = 1.5) 
        if sample[i, second_panel] > 10 and sample[i, second_panel] < 20:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'seagreen', linewidth = 1.5)  
        if sample[i, second_panel] > 0 and sample[i, second_panel] < 10:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

13-period RSI heatmap.

Dark green and red areas indicate imminent bullish and bearish reactions, respectively. RSI around 50 is grey.

Summary

To conclude, my goal is to contribute to objective technical analysis, which promotes more transparent methods and strategies that must be back-tested before implementation.

Technical analysis will lose its reputation as subjective and unscientific.

When you find a trading strategy or technique, follow these steps:

  • Put emotions aside and adopt a critical mindset.

  • Test it in the past under conditions and simulations taken from real life.

  • Try optimizing it and performing a forward test if you find any potential.

  • Transaction costs and any slippage simulation should always be included in your tests.

  • Risk management and position sizing should always be considered in your tests.

After checking the above, monitor the strategy because market dynamics may change and make it unprofitable.

Maria Urkedal York

Maria Urkedal York

2 years ago

When at work, don't give up; instead, think like a designer.

How to reframe irritation and go forward

Picture by Daniel Xavier

… before you can figure out where you are going, you need to know where you are, and once you know and accept where you are, you can design your way to where you want to be.” — Bill Burnett and Dave Evans

“You’ve been here before. But there are some new ingredients this time. What can tell yourself that will make you understand that now isn’t just like last year? That there’s something new in this August.”

My coach paused. I sighed, inhaled deeply, and considered her question.

What could I say? I simply needed a plan from her so everything would fall into place and I could be the happy, successful person I want to be.

Time passed. My mind was exhausted from running all morning, all summer, or the last five years, searching for what to do next and how to get there.

Calmer, I remembered that my coach's inquiry had benefited me throughout the summer. The month before our call, I read Designing Your Work Life — How to Thrive and Change and Find Happiness at Work from Standford University’s Bill Burnett and Dave Evans.

A passage in their book felt like a lifeline: “We have something important to say to you: Wherever you are in your work life, whatever job you are doing, it’s good enough. For now. Not forever. For now.”

As I remembered this book on the coaching call, I wondered if I could embrace where I am in August and say my job life is good enough for now. Only temporarily.

I've done that since. I'm getting unstuck.

Here's how you can take the first step in any area where you feel stuck.

How to acquire the perspective of "Good enough for now" for yourself

We’ve all heard the advice to just make the best of a bad situation. That´s not bad advice, but if you only make the best of a bad situation, you are still in a bad situation. It doesn’t get to the root of the problem or offer an opportunity to change the situation. You’re more cheerfully navigating lousiness, which is an improvement, but not much of one and rather hard to sustain over time.” — Bill Burnett and Dave Evans

Reframing Burnett at Evans says good enough for now is the key to being happier at work. Because, as they write, a designer always has options.

Choosing to believe things are good enough for now is liberating. It helps us feel less victimized and less judged. Accepting our situation helps us become unstuck.

Let's break down the process, which designers call constructing your way ahead, into steps you can take today.

Writing helps get started. First, write down your challenge and why it's essential to you. If pen and paper help, try this strategy:

  • Make the decision to accept the circumstance as it is. Designers always begin by acknowledging the truth of the situation. You now refrain from passing judgment. Instead, you simply describe the situation as accurately as you can. This frees us from negative thought patterns that prevent us from seeing the big picture and instead keep us in a tunnel of negativity.

  • Look for a reframing right now. Begin with good enough for the moment. Take note of how your body feels as a result. Tell yourself repeatedly that whatever is occurring is sufficient for the time being. Not always, but just now. If you want to, you can even put it in writing and repeatedly breathe it in, almost like a mantra.

  • You can select a reframe that is more relevant to your situation once you've decided that you're good enough for now and have allowed yourself to believe it. Try to find another perspective that is possible, for instance, if you feel unappreciated at work and your perspective of I need to use and be recognized for all my new skills in my job is making you sad and making you want to resign. For instance, I can learn from others at work and occasionally put my new abilities to use.

  • After that, leave your mind and act in accordance with your new perspective. Utilize the designer's bias for action to test something out and create a prototype that you can learn from. Your beginning point for creating experiences that will support the new viewpoint derived from the aforementioned point is the new perspective itself. By doing this, you recognize a circumstance at work where you can provide value to yourself or your workplace and then take appropriate action. Send two or three coworkers from whom you wish to learn anything an email, for instance, asking them to get together for coffee or a talk.

Choose tiny, doable actions. You prioritize them at work.

Let's assume you're feeling disconnected at work, so you make a list of folks you may visit each morning or invite to lunch. If you're feeling unmotivated and tired, take a daily walk and treat yourself to a decent coffee.

This may be plenty for now. If you want to take this procedure further, use Burnett and Evans' internet tools and frameworks.

Developing the daily practice of reframing

“We’re not discontented kids in the backseat of the family minivan, but how many of us live our lives, especially our work lives, as if we are?” — Bill Burnett and Dave Evans

I choose the good enough for me perspective every day, often. No quick fix. Am a failing? Maybe a little bit, but I like to think of it more as building muscle.

This way, every time I tell myself it's ok, I hear you. For now, that muscle gets stronger.

Hopefully, reframing will become so natural for us that it will become a habit, and not a technique anymore.

If you feel like you’re stuck in your career or at work, the reframe of Good enough, for now, might be valuable, so just go ahead and try it out right now.

And while you’re playing with this, why not think of other areas of your life too, like your relationships, where you live — even your writing, and see if you can feel a shift?

Katrine Tjoelsen

Katrine Tjoelsen

2 years ago

8 Communication Hacks I Use as a Young Employee

Learn these subtle cues to gain influence.

Hate being ignored?

As a 24-year-old, I struggled at work. Attention-getting tips How to avoid being judged by my size, gender, and lack of wrinkles or gray hair?

I've learned seniority hacks. Influence. Within two years as a product manager, I led a team. I'm a Stanford MBA student.

These communication hacks can make you look senior and influential.

1. Slowly speak

We speak quickly because we're afraid of being interrupted.

When I doubt my ideas, I speak quickly. How can we slow down? Jamie Chapman says speaking slowly saps our energy.

Chapman suggests emphasizing certain words and pausing.

2. Interrupted? Stop the stopper

Someone interrupt your speech?

Don't wait. "May I finish?" No pause needed. Stop interrupting. I first tried this in Leadership Laboratory at Stanford. How quickly I gained influence amazed me.

Next time, try “May I finish?” If that’s not enough, try these other tips from Wendy R.S. O’Connor.

3. Context

Others don't always see what's obvious to you.

Through explanation, you help others see the big picture. If a senior knows it, you help them see where your work fits.

4. Don't ask questions in statements

“Your statement lost its effect when you ended it on a high pitch,” a group member told me. Upspeak, it’s called. I do it when I feel uncertain.

Upspeak loses influence and credibility. Unneeded. When unsure, we can say "I think." We can even ask a proper question.

Someone else's boasting is no reason to be dismissive. As leaders and colleagues, we should listen to our colleagues even if they use this speech pattern.

Give your words impact.

5. Signpost structure

Signposts improve clarity by providing structure and transitions.

Communication coach Alexander Lyon explains how to use "first," "second," and "third" He explains classic and summary transitions to help the listener switch topics.

Signs clarify. Clarity matters.

6. Eliminate email fluff

“Fine. When will the report be ready? — Jeff.”

Notice how senior leaders write short, direct emails? I often use formalities like "dear," "hope you're well," and "kind regards"

Formality is (usually) unnecessary.

7. Replace exclamation marks with periods

See how junior an exclamation-filled email looks:

Hi, all!
Hope you’re as excited as I am for tomorrow! We’re celebrating our accomplishments with cake! Join us tomorrow at 2 pm!
See you soon!

Why the exclamation points? Why not just one?

Hi, all.
Hope you’re as excited as I am for tomorrow. We’re celebrating our accomplishments with cake. Join us tomorrow at 2 pm!
See you soon.

8. Take space

"Playing high" means having an open, relaxed body, says Stanford professor and author Deborah Gruenfield.

Crossed legs or looking small? Relax. Get bigger.