To achieve the given tolerance just below 10⁻⁶, we needed n≃145 in the most favourable case. Below, I show you how the n

Of course, the apparent saving of a factor 145/24≃6 in computing time is, at least partially, lost because of the need to fit the data. However, a straight line fit is, in fact, straightforward, and can be achieved with a very simple algorithm, such that the time spent in doing it is negligible. In fact, while we needed 0.0066 s to compute the integral using the midpoint rule and n=145, the time needed to compute it with a precision better than an order of magnitude was, in fact, 0.0012 s.

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sion to transfer Waller during a pandemic — something public health officials had advised against for months — has already resulted in Waller contracting Covid-19 inside the Colorado facility. But finally being released from quarantine early this week has been cold comfort for the 55-year-old woman, who could be deported to Belize as soon as this week.

As an independent journalist writing on Substack, I imagined the tech executives criticizing so-called corporate journalism might be willing to engage in a dialogue here on Big Technology. But Lonsdale and Graham ignored my emails (they’re still welcome to join the podcast). At a certain point, you wonder if it’s unfounded criticism or criticism itself they have an issue with.

Of course, the apparent saving of a factor 145/24≃6 in computing time is, at least partially, lost because of the need to fit the data. However, a straight line fit is, in fact, straightforward, and can be achieved with a very simple algorithm, such that the time spent in doing it is negligible. In fact, while we needed 0.0066 s to compute the integral using the midpoint rule and n=145, the time needed to compute it with a precision better than an order of magnitude was, in fact, 0.0012 s.

In the end, evaluating f(x) just N=3 5 7 9=24 times, we obtained a better precision with respect to the case n=145, which requires to evaluate f(x) 145 times. Not bad, isn’t it?

Being the target of bad press stings. But for those hoping to develop healthy companies, ignoring it is risky. Journalists can be overzealous, but sidelining their work because it isn’t perfect will only ensure legitimate problems go unaddressed. If Coinbase didn’t agree with the breadth of the Times’ critique, it could’ve used the moment to ask why many of its Black employees felt compelled to speak up. If some in the tech industry believe reporters are out to get them, then a dialogue — not boycott — seems like a good place to start.

Hsieh was a classic tech founder. He was experimental, quirky, and unafraid of failure. His downtown Vegas residence was a parking lot filled with Airstreams and tiny houses, and I remember visiting in 2015. After watching live-band karaoke and petting Hsieh’s pet llama, I went over to meet him. Hsieh wasn’t overly friendly, but he was gracious, an ultra-successful founder willing to let those who critique him roam free in his home.

We need dialogue now because these movements tend to pick up steam and take on lives of their own. As recent history teaches us, it can be difficult to go back. Even those who’d carry out the “go direct” mission feel uneasy about where it might lead. “I’m the thing that they’re telling people to do,” Sean Blanda, a journalist turned tech company editor, told me. “For the general public, I always think it’s a net negative when there’s less journalism.”

The allure of “going direct” is simple. Thanks to the social internet, you can now tell your story exactly as you’d like — without any criticism — instead of filtering it through reporters’ and editors’ lenses. Everyone from athletes to politicians have embraced this form of media. And some in the tech industry, after years of easy treatment from the press, are now gravitating toward it too.

Soon after Coinbase’s post went up, a chorus of tech insiders implored their peers to cut off the press, and tell their stories themselves. “Build your own media arm, hire an [editor-in-chief], and go direct,” Palantir co-founder Joe Lonsdale tweeted. “The quality of traditional publications is declining simultaneously with our need for them,” said Y-Combinator co-founder Paul Graham. “Better to say your own story than defend the one NYT writes,” said product manager Madhur Chadha.

Over Thanksgiving break, a spectacle developed over a forthcoming New York Times story about Coinbase. News of the story first appeared on Coinbase’s blog, where the company posted an email to employees warning of an impending negative article. “The story,” it said, “will allege that several Black employees had negative experiences at Coinbase over the last few years.”

Just as the Coinbase drama hit a crescendo, news of Zappos founder Tony Hsieh’s passing broke. Almost immediately, the public conversation turned from anger to love. Gratitude for Hsieh’s work, both in the tech industry and in his Las Vegas community, poured out.

Thus, in order to achieve the same precision, it is enough to compute the same integral numerically for n=3, 5, 7 and 9, then fit the data against a straight line: its intercept coincides with the estimation of the integral for n=∞. The remainder, in this case, is 1.5⨉10⁻⁷, one order of magnitude better than the one obtained with n=145!

The integral will thus be given by p[1]. Its remainder can be statistically estimated as the square root of the corresponding element of the covariance matrix cov[1][1], as

The remainder tends to zero as 1/n² when n tends to infinity. Thus, if we plot I(n) as a function of 1/n², according to the above formula, we should expect I(n) to follow a linear behaviour. Indeed, here is how I(n) evolves as a function of 1/n²: