More on Web3 & Crypto
Vitalik
4 years ago
An approximate introduction to how zk-SNARKs are possible (part 1)
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has two very powerful applications:
- Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
- Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.
But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.
Why ZK-SNARKs "should" be hard
Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.
A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.
One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?
Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.
But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.
It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.
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? There is a clever solution.
see part 2
Nabil Alouani
3 years ago
Why Cryptocurrency Is Not Dead Despite the FTX Scam
A fraud, free-market, antifragility tale
Crypto's only rival is public opinion.
In less than a week, mainstream media, bloggers, and TikTokers turned on FTX's founder.
While some were surprised, almost everyone with a keyboard and a Twitter account predicted the FTX collapse. These financial oracles should have warned the 1.2 million people Sam Bankman-Fried duped.
After happening, unexpected events seem obvious to our brains. It's a bug and a feature because it helps us cope with disasters and makes our reasoning suck.
Nobody predicted the FTX debacle. Bloomberg? Politicians. Non-famous. No cryptologists. Who?
When FTX imploded, taking billions of dollars with it, an outrage bomb went off, and the resulting shockwave threatens the crypto market's existence.
As someone who lost more than $78,000 in a crypto scam in 2020, I can only understand people’s reactions. When the dust settles and rationality returns, we'll realize this is a natural occurrence in every free market.
What specifically occurred with FTX? (Skip if you are aware.)
FTX is a cryptocurrency exchange where customers can trade with cash. It reached #3 in less than two years as the fastest-growing platform of its kind.
FTX's performance helped make SBF the crypto poster boy. Other reasons include his altruistic public image, his support for the Democrats, and his company Alameda Research.
Alameda Research made a fortune arbitraging Bitcoin.
Arbitrage trading uses small price differences between two markets to make money. Bitcoin costs $20k in Japan and $21k in the US. Alameda Research did that for months, making $1 million per day.
Later, as its capital grew, Alameda expanded its trading activities and began investing in other companies.
Let's now discuss FTX.
SBF's diabolic master plan began when he used FTX-created FTT coins to inflate his trading company's balance sheets. He used inflated Alameda numbers to secure bank loans.
SBF used money he printed himself as collateral to borrow billions for capital. Coindesk exposed him in a report.
One of FTX's early investors tweeted that he planned to sell his FTT coins over the next few months. This would be a minor event if the investor wasn't Binance CEO Changpeng Zhao (CZ).
The crypto space saw a red WARNING sign when CZ cut ties with FTX. Everyone with an FTX account and a brain withdrew money. Two events followed. FTT fell from $20 to $4 in less than 72 hours, and FTX couldn't meet withdrawal requests, spreading panic.
SBF reassured FTX users on Twitter. Good assets.
He lied.
SBF falsely claimed FTX had a liquidity crunch. At the time of his initial claims, FTX owed about $8 billion to its customers. Liquidity shortages are usually minor. To get cash, sell assets. In the case of FTX, the main asset was printed FTT coins.
Sam wouldn't get out of trouble even if he slashed the discount (from $20 to $4) and sold every FTT. He'd flood the crypto market with his homemade coins, causing the price to crash.
SBF was trapped. He approached Binance about a buyout, which seemed good until Binance looked at FTX's books.
Binance's tweet ended SBF, and he had to apologize, resign as CEO, and file for bankruptcy.
Bloomberg estimated Sam's net worth to be zero by the end of that week. 0!
But that's not all. Twitter investigations exposed fraud at FTX and Alameda Research. SBF used customer funds to trade and invest in other companies.
Thanks to the Twitter indie reporters who made the mainstream press look amateurish. Some Twitter detectives didn't sleep for 30 hours to find answers. Others added to existing threads. Memes were hilarious.
One question kept repeating in my bald head as I watched the Blue Bird. Sam, WTF?
Then I understood.
SBF wanted that FTX becomes a bank.
Think about this. FTX seems healthy a few weeks ago. You buy 2 bitcoins using FTX. You'd expect the platform to take your dollars and debit your wallet, right?
No. They give I-Owe-Yous.
FTX records owing you 2 bitcoins in its internal ledger but doesn't credit your account. Given SBF's tricks, I'd bet on nothing.
What happens if they don't credit my account with 2 bitcoins? Your money goes into FTX's capital, where SBF and his friends invest in marketing, political endorsements, and buying other companies.
Over its two-year existence, FTX invested in 130 companies. Once they make a profit on their purchases, they'll pay you and keep the rest.
One detail makes their strategy dumb. If all FTX customers withdraw at once, everything collapses.
Financially savvy people think FTX's collapse resembles a bank run, and they're right. SBF designed FTX to operate like a bank.
You expect your bank to open a drawer with your name and put $1,000 in it when you deposit $1,000. They deposit $100 in your drawer and create an I-Owe-You for $900. What happens to $900?
Let's sum it up: It's boring and headache-inducing.
When you deposit money in a bank, they can keep 10% and lend the rest. Fractional Reserve Banking is a popular method. Fractional reserves operate within and across banks.
Fractional reserve banking generates $10,000 for every $1,000 deposited. People will pay off their debt plus interest.
As long as banks work together and the economy grows, their model works well.
SBF tried to replicate the system but forgot two details. First, traditional banks need verifiable collateral like real estate, jewelry, art, stocks, and bonds, not digital coupons. Traditional banks developed a liquidity buffer. The Federal Reserve (or Central Bank) injects massive cash into troubled banks.
Massive cash injections come from taxpayers. You and I pay for bankers' mistakes and annual bonuses. Yes, you may think banking is rigged. It's rigged, but it's the best financial game in 150 years. We accept its flaws, including bailouts for too-big-to-fail companies.
Anyway.
SBF wanted Binance's bailout. Binance said no, which was good for the crypto market.
Free markets are resilient.
Nassim Nicholas Taleb coined the term antifragility.
“Some things benefit from shocks; they thrive and grow when exposed to volatility, randomness, disorder, and stressors and love adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the phenomenon, there is no word for the exact opposite of fragile. Let us call it antifragile. Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better.”
The easiest way to understand how antifragile systems behave is to compare them with other types of systems.
Glass is like a fragile system. It snaps when shocked.
Similar to rubber, a resilient system. After a stressful episode, it bounces back.
A system that is antifragile is similar to a muscle. As it is torn in the gym, it gets stronger.
Time-changed things are antifragile. Culture, tech innovation, restaurants, revolutions, book sales, cuisine, economic success, and even muscle shape. These systems benefit from shocks and randomness in different ways, but they all pay a price for antifragility.
Same goes for the free market and financial institutions. Taleb's book uses restaurants as an example and ends with a reference to the 2008 crash.
“Restaurants are fragile. They compete with each other. But the collective of local restaurants is antifragile for that very reason. Had restaurants been individually robust, hence immortal, the overall business would be either stagnant or weak and would deliver nothing better than cafeteria food — and I mean Soviet-style cafeteria food. Further, it [the overall business] would be marred with systemic shortages, with once in a while a complete crisis and government bailout.”
Imagine the same thing with banks.
Independent banks would compete to offer the best services. If one of these banks fails, it will disappear. Customers and investors will suffer, but the market will recover from the dead banks' mistakes.
This idea underpins a free market. Bitcoin and other cryptocurrencies say this when criticizing traditional banking.
The traditional banking system's components never die. When a bank fails, the Federal Reserve steps in with a big taxpayer-funded check. This hinders bank evolution. If you don't let banking cells die and be replaced, your financial system won't be antifragile.
The interdependence of banks (centralization) means that one bank's mistake can sink the entire fleet, which brings us to SBF's ultimate travesty with FTX.
FTX has left the cryptocurrency gene pool.
FTX should be decentralized and independent. The super-star scammer invested in more than 130 crypto companies and linked them, creating a fragile banking-like structure. FTX seemed to say, "We exist because centralized banks are bad." But we'll be good, unlike the centralized banking system.
FTX saved several companies, including BlockFi and Voyager Digital.
FTX wanted to be a crypto bank conglomerate and Federal Reserve. SBF wanted to monopolize crypto markets. FTX wanted to be in bed with as many powerful people as possible, so SBF seduced politicians and celebrities.
Worst? People who saw SBF's plan flaws praised him. Experts, newspapers, and crypto fans praised FTX. When billions pour in, it's hard to realize FTX was acting against its nature.
Then, they act shocked when they realize FTX's fall triggered a domino effect. Some say the damage could wipe out the crypto market, but that's wrong.
Cell death is different from body death.
FTX is out of the game despite its size. Unfit, it fell victim to market natural selection.
Next?
The challengers keep coming. The crypto economy will improve with each failure.
Free markets are antifragile because their fragile parts compete, fostering evolution. With constructive feedback, evolution benefits customers and investors.
FTX shows that customers don't like being scammed, so the crypto market's health depends on them. Charlatans and con artists are eliminated quickly or slowly.
Crypto isn't immune to collapse. Cryptocurrencies can go extinct like biological species. Antifragility isn't immortality. A few more decades of evolution may be enough for humans to figure out how to best handle money, whether it's bitcoin, traditional banking, gold, or something else.
Keep your BS detector on. Start by being skeptical of this article's finance-related claims. Even if you think you understand finance, join the conversation.
We build a better future through dialogue. So listen, ask, and share. When you think you can't find common ground with the opposing view, remember:
Sam Bankman-Fried lied.
Vitalik
4 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
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MartinEdic
3 years ago
Russia Through the Windows: It's Very Bad
And why we must keep arming Ukraine
Russian expatriates write about horrific news from home.
Read this from Nadin Brzezinski. She's not a native English speaker, so there are grammar errors, but her tale smells true.
Terrible truth.
There's much more that reveals Russia's grim reality.
Non-leadership. Millions of missing supplies are presumably sold for profit, leaving untrained troops without food or gear. Missile attacks pause because they run out. Fake schemes to hold talks as a way of stalling while they scramble for solutions.
Street men were mobilized. Millions will be ground up to please a crazed despot. Fear, wrath, and hunger pull apart civilization.
It's the most dystopian story, but Ukraine is worse. Destruction of a society, country, and civilization. Only the invaders' corruption and incompetence save the Ukrainians.
Rochester, NY. My suburb had many Soviet-era Ukrainian refugees. Their kids were my classmates. Fifty years later, many are still my friends. I loved their food and culture. My town has 20,000 Ukrainians.
Grieving but determined. They don't quit. They won't quit. Russians are eternal enemies.
It's the Russian people's willingness to tolerate corruption, abuse, and stupidity by their leaders. They are paying. 65000 dead. Ruined economy. No freedom to speak. Americans do not appreciate that freedom as we should.
It lets me write/publish.
Russian friends are shocked. Many are here because their parents escaped Russian anti-semitism and authoritarian oppression. A Russian cultural legacy says a strongman's methods are admirable.
A legacy of a slavery history disguised as serfdom. Peasants and Princes.
Read Tolstoy. Then Anna Karenina. The main characters are princes and counts, whose leaders are incompetent idiots with wealth and power.
Peasants who die in their wars due to incompetence are nameless ciphers.
Sound familiar?
Scott Stockdale
3 years ago
A Day in the Life of Lex Fridman Can Help You Hit 6-Month Goals
The Lex Fridman podcast host has interviewed Elon Musk.
Lex is a minimalist YouTuber. His videos are sloppy. Suits are his trademark.
In a video, he shares a typical day. I've smashed my 6-month goals using its ideas.
Here's his schedule.
Morning Mantra
Not woo-woo. Lex's mantra reflects his practicality.
Four parts.
Rulebook
"I remember the game's rules," he says.
Among them:
Sleeping 6–8 hours nightly
1–3 times a day, he checks social media.
Every day, despite pain, he exercises. "I exercise uninjured body parts."
Visualize
He imagines his day. "Like Sims..."
He says three things he's grateful for and contemplates death.
"Today may be my last"
Objectives
Then he visualizes his goals. He starts big. Five-year goals.
Short-term goals follow. Lex says they're year-end goals.
Near but out of reach.
Principles
He lists his principles. Assertions. His goals.
He acknowledges his cliche beliefs. Compassion, empathy, and strength are key.
Here's my mantra routine:
Four-Hour Deep Work
Lex begins a four-hour deep work session after his mantra routine. Today's toughest.
AI is Lex's specialty. His video doesn't explain what he does.
Clearly, he works hard.
Before starting, he has water, coffee, and a bathroom break.
"During deep work sessions, I minimize breaks."
He's distraction-free. Phoneless. Silence. Nothing. Any loose ideas are typed into a Google doc for later. He wants to work.
"Just get the job done. Don’t think about it too much and feel good once it’s complete." — Lex Fridman
30-Minute Social Media & Music
After his first deep work session, Lex rewards himself.
10 minutes on social media, 20 on music. Upload content and respond to comments in 10 minutes. 20 minutes for guitar or piano.
"In the real world, I’m currently single, but in the music world, I’m in an open relationship with this beautiful guitar. Open relationship because sometimes I cheat on her with the acoustic." — Lex Fridman
Two-hour exercise
Then exercise for two hours.
Daily runs six miles. Then he chooses how far to go. Run time is an hour.
He does bodyweight exercises. Every minute for 15 minutes, do five pull-ups and ten push-ups. It's David Goggins-inspired. He aims for an hour a day.
He's hungry. Before running, he takes a salt pill for electrolytes.
He'll then take a one-minute cold shower while listening to cheesy songs. Afterward, he might eat.
Four-Hour Deep Work
Lex's second work session.
He works 8 hours a day.
Again, zero distractions.
Eating
The video's meal doesn't look appetizing, but it's healthy.
It's ground beef with vegetables. Cauliflower is his "ground-floor" veggie. "Carrots are my go-to party food."
Lex's keto diet includes 1800–2000 calories.
He drinks a "nutrient-packed" Atheltic Greens shake and takes tablets. It's:
One daily tablet of sodium.
Magnesium glycinate tablets stopped his keto headaches.
Potassium — "For electrolytes"
Fish oil: healthy joints
“So much of nutrition science is barely a science… I like to listen to my own body and do a one-person, one-subject scientific experiment to feel good.” — Lex Fridman
Four-hour shallow session
This work isn't as mentally taxing.
Lex planned to:
Finish last session's deep work (about an hour)
Adobe Premiere podcasting (about two hours).
Email-check (about an hour). Three times a day max. First, check for emergencies.
If he's sick, he may watch Netflix or YouTube documentaries or visit friends.
“The possibilities of chaos are wide open, so I can do whatever the hell I want.” — Lex Fridman
Two-hour evening reading
Nonstop work.
Lex ends the day reading academic papers for an hour. "Today I'm skimming two machine learning and neuroscience papers"
This helps him "think beyond the paper."
He reads for an hour.
“When I have a lot of energy, I just chill on the bed and read… When I’m feeling tired, I jump to the desk…” — Lex Fridman
Takeaways
Lex's day-in-the-life video is inspiring.
He has positive energy and works hard every day.
Schedule:
Mantra Routine includes rules, visualizing, goals, and principles.
Deep Work Session #1: Four hours of focus.
10 minutes social media, 20 minutes guitar or piano. "Music brings me joy"
Six-mile run, then bodyweight workout. Two hours total.
Deep Work #2: Four hours with no distractions. Google Docs stores random thoughts.
Lex supplements his keto diet.
This four-hour session is "open to chaos."
Evening reading: academic papers followed by fiction.
"I value some things in life. Work is one. The other is loving others. With those two things, life is great." — Lex Fridman
Katrine Tjoelsen
3 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.
