One explicitly recites the Ultraviolet Catastrophe prompted Planck story, complete with Rayleigh's incomplete formula.

One essentially matches the story in section 2, using the lesser version of Rayleigh's formula, but (just like the story) does not explicitly tie Planck's work to it. (That textbook notes "an act of desperation" is a quote from one of Planck's letters.)

The third one is interesting! It says that "late nineteenth century physicists tried to understand the shape of the blackbody spectrum [...] using their knowledge of thermodynamics and electromagnetic waves. Their efforts ended in failure." This third text never mentions Rayleigh by name and doesn't specifically show "Rayleigh's Lesser Formula", but it does graph that formula vs. the observed blackbody radiation (interestingly, as a function of frequency instead of wavelength).

The text then eventually says that in 1900, Planck used a photon argument "to make a theoretical prediction that is in excellent agreement with the experimental spectrum". It does not explicitly state cause and effect, but it's kinda implied from the structure of the writing.

Reading into the third text a smidge, it feels like the result of wanting to use the Rayleigh/Catastrophe story and yet knowing it wasn't quite true.

The reader goes to ExamplePrint and buys the book.

ExamplePrint prints a softcover copy of the book on the spot and ships it out to the reader.

The user pays ExamplePrint, who pays the author some fraction of the user's money.

The reader is a customer of ExamplePrint and reading the author's book.

This is the analogy Apple would like to use for their app store. Apple's print time is almost instantaneous and the marginal costs are closer to zero.

There exists the Rogers Test in trademark law that says that, for an /artistic work/, all a defendant has to do is show that a) the trademark is relevant to the artistic work, and b) the title is not explicitly misleading (to make the audience think the work is created/supported by the trademark holder).

The Rogers Test, reserved for artistic work, is gentler than normal trademark defense. Bad Spaniels chew toy passed this test easily.

The Supreme Court ruled 9-0 that, because the chew toy is released by the Bad Spaniels /brand/, the Rogers /artistic work/ analysis is not appropriate.

Instead, it should be litigated as a brand vs. brand trademark dispute.

In a brand vs. brand dispute, Jack Daniels will have to instead prove that the Bad Spaniels brand is likely to cause confusion with regards to Jack Daniels brand's involvement in the product.

This is a higher bar to clear than Rogers test, because the trademark doesn't have to be explicitly confusing; it just needs to be likely.

I'm not a lawyer or a judge, but I don't think Jack Daniels will prevail even with the stricter standard.

(IMO,) this ruling is barely going to matter in the long run: if the Bad Spaniels chew bottle was sold by Bob's Novelties and did not included the word "brand" after "Bad Spaniels", then the Rogers test would still apply.

A decade or so later, Apple was on the tail end of a long, slow, downward slide. The team wasn't happy with the current state of their Mac operating system, and bought out NeXT to use their software as the basis of its replacement (Mac OS X).

Jobs, as CEO of NeXT, came back to Apple as a consultant, but was CEO again in a matter of years.

> OGL 1.1 makes clear it only covers material created for use in or as TTRPGs, and those materials are only ever permitted as printed media or static electronic files (like epubs and PDFs). Other types of content, like videos and video games, are only possible through the Wizards of the Coast Fan Content Policy or a custom agreement with us.

The Fan Content Policy is:

https://company.wizards.com/en/legal/fancontentpolicy

Which says that:

> You can’t require payments, surveys, downloads, subscriptions, or email registration to access your Fan Content;

> You can’t sell or license your Fan Content to any third parties for any type of compensation; and

> Your Fan Content must be free for others (including Wizards) to view, access, share, and use without paying you anything, obtaining your approval, or giving you credit.

> You can, however, subsidize your Fan Content by taking advantage of sponsorships, ad revenue, and donations—so long as it doesn’t interfere with the Community’s access to your Fan Content.

All of this exists (IMO) because game mechanics aren't subject to copyright, so you can, if you'd like, read these two sets of rules as Hasbro saying, "This is what we're willing to let you do without having to get a lawyer to defend yourself in court, even if it's legally allowed."

Note, though, that in GP's post, "places and characters from one of the world say Ansalon" very much are covered by WotC's copyrights (and probably some trademarks too).

https://www.reddit.com/r/dwarffortress/comments/b0mzog/offic...

https://www.deadiversion.usdoj.gov/21cfr/cfr/1308/1308_12.ht...

All journalists are biased. Pretending they can be unbiased is silly.

Beyond that, a journalist specialized in CS writing about the ecological impact of technology is no longer "sticking to what they've studied and know" any more than a sportswriter would be writing about the ecological impact of a new stadium.

> Apple dominates the global handset market by capturing 66% of industry profits and 32% of the overall handset revenue.

Samsung and Huawei are second and third with about 20% and 10%, respectively. The three companies combine for about 95% of the profits.

https://www.counterpointresearch.com/apple-continues-lead-gl...

In the same quarter, Apple had 12% of the global market sales, against 21% by Samsung and 18% by Huawei. They combine for 51% of the sales.

https://www.counterpointresearch.com/global-smartphone-share...

So, that quarter, companies representing half of the worldwide cellphone sales combined for 5% of the profit.

Apple sold 12% of the phones and captured 32% of the revenue but 66% of the profit.

Apple is clearly able to sell its phones at a unique premium; I am not sure of a better way to measure "attractive".

One thing I tell my high-school students: mathematics always looks harder than it actually is. One of the essential skills in succeeding in math is looking at a page of arcane "stuff" and having your reaction be, "Whoa! Can't wait to learn what this means," rather than, "Whoa! This looks so complicated!"

Mathematical is its own language that has developed across continents and millennia. It has its quirks and foibles, but overall, community consensus has guided its notation. Mathematicians want things to be simple and "make sense", especially the notation they use. It's never as terrible as it looks.

Sigma specifically is a Greek letter, but the notation is not Greek. Like a large amount of modern mathematical notation, the convention came from Leonhard Euler in the 18th century. It was a disambiguation choice because the letter S was overloaded.

Single-symbol identifiers are enormously popular in mathematics because mathematics is not computing. Because math is (even now) essentially a handwritten subject, its design plays to the strengths of handwriting. Line size, height, and character layout are essentially freeform. Character accents and modifiers are easy. discrete_sum would never fly in a handwritten world, just like ∑ wouldn't pass code review.

It seems right to me. It's a relatively small fine; Apple makes a few hundred Euros in profit per phone. I'm not sure how many iPhones are in France, but I'd venture to guess this is less than 2 Euros per device.

[1] https://news.ycombinator.com/item?id=22204995

https://news.ycombinator.com/item?id=22204995

https://news.ycombinator.com/item?id=22204995

Why do I like it? I am, as klodolph notes [1], a dyed-in-the-wool algebraist. It's where I find the most beauty and joy in mathematics.

[1] https://news.ycombinator.com/item?id=22202606

This invention/discovery is a fundamental development in abstract algebra, not a terminal one. Quaternions are just a jumping-off point, and I've always found the Caley-Dickenson construction that pauldraper explains[2] absolutely beautiful.

[2] https://news.ycombinator.com/item?id=22202513

Why would I want it specifically as a tattoo? jfengel points out the special history of that specific equation[3]: it was (allegedly) carved into a bridge in Dublin when Hamilton stumbled onto it, but the carving is gone. Kinda fitting to give it new permanence.

[3] https://news.ycombinator.com/item?id=22202513

So, putting it all together: it's a fundamental development in abstract algebra, which is my jam. It's could have been permanently inscribed in a bridge, but that's been lost to time, so giving it new permanency seems fitting.

Also, it's practical. My first thought was actually the Cayley table for the Klein four-group[4], but that would be a lot harder to get tattooed in a nice visible way. How I went from there to Hamilton's quaternion equation is left as an exercise to the reader. (If you're new to Cayley tables, they're just fancy times tables. Replace "e" with 1.)

[4] https://en.wikipedia.org/wiki/Klein_four-group#Presentations

Two years ago, my wife asked me, "If you had to get a math equation tattooed on your body, what would it be?" I answered, "i^2 = j^2 = k^2 = ijk = -1".

I felt a brief flush of anger when I saw this headline.

This is an extraordinarily good article that should be read by pretty much anyone doing graphics programming.

The first step (authenticating) returns a token with your app id, user email address, a unique user id, an expiration time 5m from issuance, and various other info.

Suppose the token is not verified. If the app only uses the email to identify a client, then a malicious/compromised user could pass your app a forged token to access another user's account.

If the app uses email and id, but not the other fields, then a replay attack is possible on a compromised user: the eavesdropper could simply send along an intercepted token to identify as the compromised user. If the timestamp is checked, this gets harder but is still doable.

The other benefit: once you have verified the token, you can also refresh it in the future (1/day max) to silently re-verify the user. If you instead "re-"verify by repeating the initial credential issuance process, the user will be prompted for 2FA verification.

"iMessages" sent to your phone number will be translated to SMS.

iMessages sent to your email address will still be delivered to the account associated with that email address. They can be accessed on pretty much any modern apple device associated with that account.

It's rare that people intentionally iMessage an email address, but the interface is opaque enough that it's essentially impossible on an existing text chain to tell that you did (unless you're specifically looking for that information).

The behavior as implemented makes sense provided that every user made an intentional and informed choice when choosing to message a friend via phone number or email. That is, of course, not the case (and is not helped by Siri sometimes silently deciding to use a contact's email over their phone number).