pflats

I was curious, so I grabbed three undergraduate-level physics texts I had nearby.

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.

Suppose an author uploads their book to ExamplePrint Inc, a one stop shop that prints made-to-order books for customers.

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.

A bit of an oversimplification and slightly wrong, but the problem is essentially that it is a Bad Spaniels brand dog toy, parodying the sound-a-like Jack Daniels brand whiskey.

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.

More specifically, Steve Jobs founded NeXT after Apple pushed him out in the late 80s.

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.

Zuckerberg almost always refers to one specific person; Cuban is a last name of an investor and also describes things related to the nation of Cuba.

Not true. One of the very first lines there states that:

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).

20% is going to the publisher. They paid for the Steam version, including hiring the graphics and sound people. They're also handling customer support for the paid version.

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

The study also does not claim to show a causal relationship.

To add a little detail to what others said, amphetamine and its salts are explicitly a Schedule II controlled substance in the US.

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

Isn't there a serious risk of bias, there, though? For example, if a journalist is specialized in CS and have to write about the ecological impact of technology, you can expect them to be biased in favor of technology, even in good faith.

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.

This is the case; it really shouldn't be downvoted.

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".

Also, curse the Greeks for not using more idiomatic variables. ∑ would never pass code review, what an entirely unreadable identifier

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.

I'm sort of conflicted about the fine hitting now, as a result. If they were still being intransigent about the issue, sure, but they've already fixed it...

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.

Thanks for writing this! It's spot on. I referenced it in a post upthread[1].

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

Thanks for writing this! I referenced it in a reply upthread for why I like the equation.

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

Thanks for writing this. It was indeed a large part of why I like it. I added more detail in a reply to the parent post.

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

I got busy, so I wanna say thanks to everyone who tagged in for me. So many great answers. I'll link a few that speak the most to my own feelings.

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

I'm a pure math dude at heart, even if I don't get to do it much any more.

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.

It depends on what the app does and how it does it.

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.

The process deregisters the phone number from the account; it does not shut down the entire iCloud account or disable iMessage entirely.

"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).

I wouldn't be surprised if there are a number of confounding factors that skew male, such TV shows/movies/video games marketed to men that feature Iran and/or the region.

I really like it, but just a heads-up: the directions threw me for a solid 15-30 seconds.

"Click a piece to select it, then click on the board to place it."

Okay, cool! I clicked on the King's Pawn, then e4. The king's pawn disappeared, and then... nothing. I clicked e3. I clicked e4 again and then... e5? e2? Nope.

Okay, maybe something went wrong. Let's try with the queen's pawn. d2, pawn goes away. d4? d3? Nope.

I re-read the directions: "Click a piece to select it, then click on the board to place it."

Weird. The pawn went away instead of being selected. How do I select a pawn? Click f2. Nope.

At that point, I look again at the pieces below the board, and click on the pawn. It's selected! I click on e4. It's on the board! Okay, I get this now, but it's not what I expected.

I see what you're doing with the controls, but I think it's a poor match for your default state. When I see a chess board in starting position, my instinct is to move a piece, not to find a way to add new pieces to the board.

My thoughts:

If you want to keep the controls the same, I'd start with an empty board and maybe clarify the directions a smidge. I'd try something like:

  To place a piece, first select it from the case, then click any empty square on the board.

  To remove an existing piece from the board, click once on it.

  Use the buttons below for standard starting position or to import a FEN position.

I went to the National Review (the conservative magazine) probably because they're @NRO on twitter.

I teach mathematics and write math curriculum professionally, and have literally taught the lesson I describe above for the better part of a decade. I say "we" in that post because in more than half of those classes, I did not teach it alone, but in a co-taught inclusion class for special education and general education students together. None of the classes where I used this lesson was an "honors"/"accelerated"/"pre-AP"/etc. class.

Every single one of those students was able to derive the quadratic equation by completing the square. It was not easy for some of them, but every single one did it.

Your parenthetical also implies to me that you think that the "truly disadvantaged" have less "mathematical skill". I would encourage you to reflect on that.

Huh, I was part of a study during my brain MRIs at NYU Lagone. I wonder if my brain is in there.

The problem with deriving the quadratic equation that way is that for most people, that is a lot of symbols to keep track of, and you have to not only do an unintuitive "completing the square" step but you have to unintuitively do it fully generically.

"Unintuitive" depends entirely on your introduction to the topic. If you're already completing the square, using it to solve quadractic equations you cannot factor is not unintuitive.

As far as doing it fully generically, well, how else do you get a generic formula? When teaching this, we would do some completing the square to solve quadractics, and then tell our students:

"You know, this is annoying to have to complete the square EVERY TIME. What if we just decided to solve it the really hard way once, with A, B, and C in the equation instead of the numbers, and see what we get?"

To me it is obvious that the method in the article is far superior than teaching completing the square.

I disagree. I would need some convincing that "two numbers that multiply to C and sum to B must have an average of B/2, so they must be B/2 + z and B/2 - z, so (B/2 + z)(B/2 - z) = C" is by any means obviously superior to completing the square. Neither is immediately intuitive; both will require prompting and teaching by the teacher. Completing the square has uses beyond proving the quadratic theorem; this does not.

I should say: I find this an incredibly cool and level-appropriate proof of the quadratic equation, but I think its merits as an improvement in pedagogy are dubious.

You are correct. It is generally expected to be part of an Algebra I curriculum (as per Common Core Appendix A's Traditional Pathway).

Common Core High School: Algebra » Reasoning with Equations & Inequalities » Solve equations and inequalities in one variable. » 4 » a

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

http://www.corestandards.org/Math/Content/HSA/REI/B/4/a/

The part that really pisses me off is the "10 strikes and we wipe your phone bit". That happened to me too on an infrequently used iphone last year.

This is an optional setting, and I'm relatively certain it used to be off by default. I think my newest iPhone specifically prompted me about it during setup.

iPads can use GraphNCalc83[1] and Apple Classroom on a teacher iPad/Mac to restrict students to the app[2]. I'm not sure if there's an android equivalent.

I still find using a touch screen much more frustrating than a calculator with physical buttons, but this is a legit alternative.

[1] https://acornaircraft.com/graphncalc83.html

[2] https://support.apple.com/guide/classroom/manage-app-usage-a...