> Unlike other ranking functions, ntile() ignores ties: it will create evenly sized buckets even if the same value of x ends up in different buckets.

But you do need homogenous coordinates if you want to include translations (fixed distance shifts, such as moving the camera) in the set of operations you can represent as linear transformations and thereby gain all the benefits of linear algebra, including the benefit of being able to include them in a series of operations that you can represent with a single transformation matrix.

Consider a transformation f where we wish to move x-y coordinates s units to the right. In 2d, we could express it as:

f(x, y) = (x + s, y)

But that transformation is affine not linear. There is no way to generate the value s as a linear combination of the inputs x and y. So, our workaround is to embed the x-y plane into 3d space at z=1. Then we can move (x,y,1) points in that plane s units to the right using this transformation:

f(x, y, z) = (x + s*z, y, z)

This new transformation is linear: it maps (0,0,0) to itself. But it maps our embedded 2d plane's origin (0,0,1) to (s,0,1), shifting it right by s units, as we want.

The matrix form of that transformation is:

    [[1 0 s]
     [0 1 0]
     [0 0 1]]

[1] https://carnegiemnh.org/collected-day-1959/

So, until the ultimate query language is developed, I'll take SQL with pipes. It's an easy sell and good enough to eliminate 90% of my gripes about SQL.

I will give you approximately twenty delightful novels where the prose and the stories are both excellent: Patrick O’Brian’s Aubrey–Maturin series.

I avoided these books for the longest time because I didn't believe I was the kind of person who would read “books about tall ships.” But so many people recommend these particular books because of the masterly writing that I tried the first, Master and Commander. Immediately, I was taken by O’Brian’s writing: vivid, lively, and engaging, while also utterly precise.

Give that first novel a try. It’s not easy, but it is oh so rewarding.

Edited to add some examples from the first novel:

“I have never yet known a man admit that he was either rich or asleep: perhaps the poor man and the wakeful man have some great moral advantage.”

“Where there was no equality there was no companionship: when a man was obliged to say ‘Yes, sir,’ his agreement was of no worth even if it happened to be true.”

“He held up two fingers, in case a landman might not fully comprehend so great a number.”

“But you know as well as I, patriotism is a word; and one that generally comes to mean either my country, right or wrong, which is infamous, or my country is always right, which is imbecile.”

Yes. When people make mistakes, they sometimes fall into holes that are hard to climb out of. It is in society’s interest to place ladders in these holes so that these unfortunate people can climb out and become productive members of society.

Instead, we have self-interested parties who have figured out how to extract rents from keeping people trapped in holes. Some of these parties are preventing ladders from being built. Others are destroying existing ladders. Others still are even inventing deeper, stickier holes—crypto scams, ubiquitous gambling, addictive gas-station drugs, dopamine-hit apps—to trap even greater numbers of their fellow human beings.

When a society allows the suffering of others to become a profitable business model, good things rarely follow.

Pittsburgh has most of the benefits of a larger city without most of the problems. Its infrastructure is in many ways over-provisioned, being built for past industry and a larger population (but the maintenance burden is catching up). Its unusually hilly and berivered geography has allowed its neighborhoods to escape homogenization and retain their individual ethnic characters. And the setting, with rivers, bridges, trails, forests, is beautiful. Plus the airport recently got overhauled to meet the region’s actual needs, making it way more convenient.

Oh, if you're in to sports, Pittsburgh has some great teams and a great fan base.

Yeah, I like the ’Burgh.

The tragedy is that we could have a society that gives people more opportunities to escape the downward pull of chance gone wrong early in life. Maybe someday we'll get there.

And, yep, it's worth a read.

Do you really mean this? Or do you mean "When you blog, be honest. Don't pretend to understand things you don't."?

Blogging about things you are learning about, especially if you invite feedback, is a great way to learn and to build a shared understanding within a larger community.

But I agree 100% on the fake-it-till-you-make-it posts on blogs and LinkedIn. That stuff is a blight on the web.

ADDED a concrete example: Consider this post: https://blog.moertel.com/posts/2026-07-23-on-the-nature-and-.... Do you think that posts like this are useful? Or net harmful?

It is like the difference between multiple-choice and essay exams. In the former, the questions you are asked reveal much about the structure of the subject to be explored and of the relative importance of its facets and the many nuances within. In the latter, you are on your own: you must conceive of a coherent map, render its form onto a blank sheet, and populate it with what is important, with everything being sensibly connected.

It is surprisingly difficult work, but so is lifting weights. That is precisely why I insist on doing it myself. If I let an AI write for me, it would be the same as letting a robot lift weights for me. Yeah, it would be easier, but I would not get stronger, nor would I gain the confidence and self discipline that comes from doing hard things.

Comments URL: https://news.ycombinator.com/item?id=49287481

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Comments URL: https://news.ycombinator.com/item?id=49280863

Points: 2

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https://xcancel.com/JeffDean/status/2085034604172603724

In short, they are in the business of using AI to automate the discovery of useful knowledge, not to sell general-purpose AI capabilities that could be directly used in troubling ways.