War's Human Cost
I didn't start crying until I was outside a McDonald's in an Olempin, Poland rest area on highway S17.

Children pick toys at a refugee center, Olempin, Poland, March 4, 2022.

Refugee children, mostly alone with their mothers, but occasionally with a gray-haired grandfather or non-Ukrainian father, were coaxed into picking a toy from boxes provided by a kind-hearted company and volunteers.
I went to Warsaw to continue my research on my family's history during the Holocaust. In light of the ongoing Ukrainian conflict, I asked former colleagues in the US Department of Defense and Intelligence Community if it was safe to travel there. They said yes, as Poland was a NATO member.
I stayed in a hotel in the Warsaw Ghetto, where 90% of my mother's family was murdered in the Holocaust. Across the street was the first Warsaw Judenrat. It was two blocks away from the apartment building my mother's family had owned and lived in, now dilapidated and empty.

Building of my great-grandfather, December 2021.

A mass grave of thousands of rocks for those killed in the Warsaw Ghetto, I didn't cry when I touched its cold walls.

Warsaw Jewish Cemetery, 200,000–300,000 graves.

Mass grave, Warsaw Jewish Cemetery.

My mother's family had two homes, one in Warszawa and the rural one was a forest and sawmill complex in Western Ukraine. For the past half-year, a local Ukrainian historian had been helping me discover faint traces of her family’s life there — in fact, he had found some people still alive who remembered the sawmill and that it belonged to my mother’s grandfather. The historian was good at his job, and we had become close.

My historian friend, December 2021, talking to a Ukrainian.

With war raging, my second trip to Warsaw took on a different mission. To see his daughter and one-year-old grandson, I drove east instead of to Ukraine. They had crossed the border shortly after the war began, leaving men behind, and were now staying with a friend on Poland's eastern border.
I entered after walking up to the house and settling with the dog. The grandson greeted me with a huge smile and the Ukrainian word for “daddy,” “Tato!” But it was clear he was awaiting his real father's arrival, and any man he met would be so tentatively named.
After a few moments, the boy realized I was only a stranger. He had musical talent, like his mother and grandfather, both piano teachers, as he danced to YouTube videos of American children's songs dubbed in Ukrainian, picking the ones he liked and crying when he didn't.

Songs chosen by my historian friend's grandson, March 4, 2022

He had enough music and began crying regardless of the song. His mother picked him up and started nursing him, saying she was worried about him. She had no idea where she would live or how she would survive outside Ukraine. She showed me her father's family history of losses in the Holocaust, which matched my own research.
After an hour of drinking tea and trying to speak of hope, I left for the 3.5-hour drive west to Warsaw.
It was unlike my drive east. It was reminiscent of the household goods-filled carts pulled by horses and people fleeing war 80 years ago.

Jewish refugees relocating, USHMM Holocaust Encyclopaedia, 1939.

The carefully chosen trinkets by children to distract them from awareness of what is really happening and the anxiety of what lies ahead, made me cry despite all my research on the Holocaust. There is no way for them to communicate with their mothers, who are worried, absent, and without their fathers.
It's easy to see war as a contest of nations' armies, weapons, and land. The most costly aspect of war is its psychological toll. My father screamed in his sleep from nightmares of his own adolescent trauma in Warsaw 80 years ago.

Survivor father studying engineering, 1961.

In the airport, I waited to return home while Ukrainian public address systems announced refugee assistance. Like at McDonald's, many mothers were alone with their children, waiting for a flight to distant relatives.
That's when I had my worst trip experience.
A woman near me, clearly a refugee, answered her phone, cried out, and began wailing.
The human cost of war descended like a hammer, and I realized that while I was going home, she never would

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Musk’s purchase of Twitter has sealed his bond with the American right—whether the platform’s left-leaning employees and users like it or not.

Elon Musk's pursuit of Twitter Inc. began earlier this month as a joke. It started slowly, then spiraled out of control, culminating on April 25 with the world's richest man agreeing to spend $44 billion on one of the most politically significant technology companies ever. There have been bigger financial acquisitions, but Twitter's significance has always outpaced its balance sheet. This is a unique Silicon Valley deal.

To recap: Musk announced in early April that he had bought a stake in Twitter, citing the company's alleged suppression of free speech. His complaints were vague, relying heavily on the dog whistles of the ultra-right. A week later, he announced he'd buy the company for $54.20 per share, four days after initially pledging to join Twitter's board. Twitter's directors noticed the 420 reference as well, and responded with a “shareholder rights” plan (i.e., a poison pill) that included a 420 joke.

Musk - Patrick Pleul/Getty Images

No one knew if the bid was genuine. Musk's Twitter plans seemed implausible or insincere. In a tweet, he referred to automated accounts that use his name to promote cryptocurrency. He enraged his prospective employees by suggesting that Twitter's San Francisco headquarters be turned into a homeless shelter, renaming the company Titter, and expressing solidarity with his growing conservative fan base. “The woke mind virus is making Netflix unwatchable,” he tweeted on April 19.

But Musk got funding, and after a frantic weekend of negotiations, Twitter said yes. Unlike most buyouts, Musk will personally fund the deal, putting up up to $21 billion in cash and borrowing another $12.5 billion against his Tesla stock.

Free Speech and Partisanship

Percentage of respondents who agree with the following

The deal is expected to replatform accounts that were banned by Twitter for harassing others, spreading misinformation, or inciting violence, such as former President Donald Trump's account. As a result, Musk is at odds with his own left-leaning employees, users, and advertisers, who would prefer more content moderation rather than less.

Dorsey - Photographer: Joe Raedle/Getty Images

Previously, the company's leadership had similar issues. Founder Jack Dorsey stepped down last year amid concerns about slowing growth and product development, as well as his dual role as CEO of payments processor Block Inc. Compared to Musk, a father of seven who already runs four companies (besides Tesla and SpaceX), Dorsey is laser-focused.

Musk's motivation to buy Twitter may be political. Affirming the American far right with $44 billion spent on “free speech” Right-wing activists have promoted a series of competing upstart Twitter competitors—Parler, Gettr, and Trump's own effort, Truth Social—since Trump was banned from major social media platforms for encouraging rioters at the US Capitol on Jan. 6, 2021. But Musk can give them a social network with lax content moderation and a real user base. Trump said he wouldn't return to Twitter after the deal was announced, but he wouldn't be the first to do so.

Trump - Eli Hiller/Bloomberg

Conservative activists and lawmakers are already ecstatic. “A great day for free speech in America,” said Missouri Republican Josh Hawley. The day the deal was announced, Tucker Carlson opened his nightly Fox show with a 10-minute laudatory monologue. “The single biggest political development since Donald Trump's election in 2016,” he gushed over Musk.

But Musk's supporters and detractors misunderstand how much his business interests influence his political ideology. He marketed Tesla's cars as carbon-saving machines that were faster and cooler than gas-powered luxury cars during George W. Bush's presidency. Musk gained a huge following among wealthy environmentalists who reserved hundreds of thousands of Tesla sedans years before they were made during Barack Obama's presidency. Musk in the Trump era advocated for a carbon tax, but he also fought local officials (and his own workers) over Covid rules that slowed the reopening of his Bay Area factory.

Teslas at the Las Vegas Convention Center Loop Central Station in April 2021. The Las Vegas Convention Center Loop was Musk's first commercial project. Ethan Miller/Getty Images

Musk's rightward shift matched the rise of the nationalist-populist right and the desire to serve a growing EV market. In 2019, he unveiled the Cybertruck, a Tesla pickup, and in 2018, he announced plans to manufacture it at a new plant outside Austin. In 2021, he decided to move Tesla's headquarters there, citing California's "land of over-regulation." After Ford and General Motors beat him to the electric truck market, Musk reframed Tesla as a company for pickup-driving dudes.

Similarly, his purchase of Twitter will be entwined with his other business interests. Tesla has a factory in China and is friendly with Beijing. This could be seen as a conflict of interest when Musk's Twitter decides how to treat Chinese-backed disinformation, as Amazon.com Inc. founder Jeff Bezos noted.

Musk has focused on Twitter's product and social impact, but the company's biggest challenges are financial: Either increase cash flow or cut costs to comfortably service his new debt. Even if Musk can't do that, he can still benefit from the deal. He has recently used the increased attention to promote other business interests: Boring has hyperloops and Neuralink brain implants on the way, Musk tweeted. Remember Tesla's long-promised robotaxis!

Musk may be comfortable saying he has no expectation of profit because it benefits his other businesses. At the TED conference on April 14, Musk insisted that his interest in Twitter was solely charitable. “I don't care about money.”

The rockets and weed jokes make it easy to see Musk as unique—and his crazy buyout will undoubtedly add to that narrative. However, he is a megabillionaire who is risking a small amount of money (approximately 13% of his net worth) to gain potentially enormous influence. Musk makes everything seem new, but this is a rehash of an old media story.

Giving through a donor-advised fund can be tax-efficient. Using a donor-advised fund can reduce your tax liability while increasing your charitable impact.

Grow Your Donations Tax-Free.

Your DAF's charitable dollars can be invested before being distributed. Your DAF balance can grow with the market. This increases grantmaking funds. The assets of the DAF belong to the charitable sponsor, so you will not be taxed on any growth.

Avoid a Windfall Tax Year.

DAFs can help reduce tax burdens after a windfall like an inheritance, business sale, or strong market returns. Contributions to your DAF are immediately tax deductible, lowering your taxable income. With DAFs, you can effectively pre-fund years of giving with assets from a single high-income event.

Make a contribution to reduce or eliminate capital gains.

One of the most common ways to fund a DAF is by gifting publicly traded securities. Securities held for more than a year can be donated at fair market value and are not subject to capital gains tax. If a donor liquidates assets and then donates the proceeds to their DAF, capital gains tax reduces the amount available for philanthropy. Gifts of appreciated securities, mutual funds, real estate, and other assets are immediately tax deductible up to 30% of Adjusted gross income (AGI), with a five-year carry-forward for gifts that exceed AGI limits.

Using Appreciated Stock as a Gift

Donating appreciated stock directly to a DAF rather than liquidating it and donating the proceeds reduces philanthropists' tax liability by eliminating capital gains tax and lowering marginal income tax.

In the example below, a donor has $100,000 in long-term appreciated stock with a cost basis of $10,000:

Using a DAF would allow this donor to give more to charity while paying less taxes. This strategy often allows donors to give more than 20% more to their favorite causes.

The information provided here is general and educational in nature. It is not intended to be, nor should it be construed as, legal or tax advice. NPT does not provide legal or tax advice. Furthermore, the content provided here is related to taxation at the federal level only. NPT strongly encourages you to consult with your tax advisor or attorney before making charitable contributions.

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.