Article URL: https://abuseofnotation.github.io/category-theory-illustrated/04_order/ Comments URL: https://news.ycombinator.com/item?id=47813668 Points: 105 # Comments: 31

Article URL: https://amiga.lychesis.net/ Comments URL: https://news.ycombinator.com/item?id=47813566 Points: 111 # Comments: 12

I've been studying interval arithmetic for the past few weeks and it's a really interesting field because while there is a ton of super interesting research published over the past decades, it has never really gotten the recognition that it deserves, IMO.One reason for this is that standard interval arithmetic has really poor handling of division by intervals containing zero. If you compute 1 / [-1, 2] in regular interval arithmetic, you get either [-∞, +∞], or you have to say that the operation is undefined. Both solutions are virtually useless. The real answer of course is [-∞, -1] U [0.5, +∞]: i.e. a union of two disjoint intervals.This is useful because you can confidently exclude a non empty set of the real numbers ([-1, 0.5]) from the set of possible values that you can get by dividing 1 by a number between -1 and 2.But this definition of interval division yields a value that is not an interval. This is a problem if you want to define a closed arithmetic system, where you can build and evaluate arbitrary expression over interval values.(This behavior extends to any non continuous function like tan() for example, which is implemented in my project - not without difficulties!)Well the obvious solution is to define your arithmetic over disjoint unions of intervals. This is the subject of a 2017 paper called "Interval Unions" by by Schichl, H., Domes, F., Montanher, T. and Kofler, K..This open-source project I made implements interval union arithmetic in TypeScript in the form of a simple interactive calculator, so you can try it out for yourself! The underlying TypeScript library is dependency free and implements interval union arithmetic over IEEE 754 double precision floats (JS native number type) with outward rounding. This guarantees accuracy of interval results in the presence of rounding issue inherent to floating point. Comments URL: https://news.ycombinator.com/item?id=47812341 Points: 186 # Comments: 36

Apple is working on an updated version of the Mac Studio that's expected at some point in 2026, and with supplies of existing machines running low, we thought we'd highlight what's next for Apple's most powerful desktop machine. Design We're not expecting Apple to redesign the ‌Mac Studio‌, and there haven't been rumors of a design update. The ‌Mac Studio‌ will continue to have an Apple TV or Mac mini-like squircle design with rounded corners. The ‌Mac Studio‌ is a much more compact desktop than the now-discontinued Mac Pro, measuring in at 3.7 inches tall and 7.7 inches wide. The current ‌Mac Studio‌ supports Thunderbolt 5, and the next version will too. There haven't been rumors of any changes to the port configuration. M5 Max and M5 Ultra Chips We're expecting the ‌Mac Studio‌ to adopt M5 Max and M5 Ultra chips. Apple already debuted the M5 Max with the MacBook Pro models that came out in March, but the M5 Ultra is still a mystery. The M5 Max has up to an 18-core CPU and 40-core GPU, with up to 614GB/s memory bandwidth. Apple says the M5 Max offers up to 30 percent faster CPU performance for pro workloads than the M4 Max. The M5 Ultra will bring even better performance, and historically, Apple's Ultra chips have been two Max chips linked together. The M5 Ultra could have up to a 36-core CPU and up to an 80-core GPU. The current ‌Mac Studio‌ has a mix of M4 Max and M3 Ultra chips because Apple didn't design an M4 Ultra chip, but the M5 cycle is expected to unify the ‌Mac Studio‌ chip options to a single generation. Faster SSD The M5 ‌MacBook Pro‌ models were updated with a faster SSD, so the ‌Mac Studio‌ could get the same SSD improvements. Apple says the updated SSD in the M5 ‌MacBook Pro‌ models is up to 2x faster than the SSD in the M4 MacBook Pro models. RAM Because of global RAM shortages, Apple discontinued the 512GB Mac Studio earlier this year. The current machine maxes out at 256GB RAM, and that's a limitation we could see with the next ‌Mac Studio‌ too. The M5 Max ‌MacBook Pro‌ supports up to 128GB RAM, so that will be the ceiling for the M5 Max ‌Mac Studio‌. The M5 Ultra model could support up to 256GB. RAM shortages are expected to continue throughout the year, because companies that manufacture memory are prioritizing orders from companies building AI servers that require huge amounts of RAM. There is little supply left for consumer products, which has caused prices to increase. Many PC and smartphone makers have raised their prices on existing machines, but Apple hasn't changed ‌Mac Studio‌ pricing. Mac Studio Shortages Apple stopped accepting orders for some ‌Mac Studio‌ configurations in early April, and they are out of stock. ‌Mac Studio‌ configurations with 128GB or 256GB of RAM can no longer be ordered, but that's not necessarily a sign that a new machine is launching imminently. Apple has been dealing with soaring DRAM and NAND flash prices, and the fact that only models with higher RAM are unavailable suggests it's a supply issue and not an indication of a refresh. Pricing There haven't been rumors of pricing increases for the ‌Mac Studio‌, so it could continue to start at $1,999, but Apple has raised the prices of other Macs this year. Starting prices for the M5 MacBook Air and the M5 Pro and M5 Max ‌MacBook Pro‌ models increased, though Apple did soften the blow with higher starting storage. It's possible the ‌Mac Studio‌ price will go up, and the entry-level machine will start with a 1TB SSD instead of a 512GB SSD. No More Mac Pro Apple discontinued the Mac Pro in late March, so the ‌Mac Studio‌ is now Apple's only pro desktop option. There was a lot of overlap between the Mac Pro and the ‌Mac Studio‌, with the Mac Pro only offering PCIe expansion slots as a differentiating feature. The ‌Mac Studio‌, Mac mini, and iMac are Apple's desktop Mac options. Release Timing It's not clear when we might see a refreshed ‌Mac Studio‌ because of the shortages that Appl

India will not require smartphone makers like Apple and Samsung to preload devices with a state-owned biometric identification app, reports Reuters. The Unique Identification Authority of India asked the IT ministry to start talks with Apple and other tech companies about the possibility of mandatory preinstallation of the Aadhaar identity app, but the IT ministry told Reuters today that it reviewed the proposal and is "not in favor" of mandating the app's preinstallation. Aadhaar is a 12-digit identity number that residents of India can apply for, and it has been issued to more than 1.34 billion residents. The number is linked to an individual's image, fingerprints, and iris scans, and it serves as proof of residence. It is used for government benefits, banking, taxes, mobile connections, and more. The Identification Authority said that the IT ministry consulted with "stakeholders from the electronics industry" before deciding not to proceed with the proposal to preload Aadhaar. India's government has asked smartphone makers to preinstall state-owned apps on devices six times over the last two years, according to Reuters. Smartphone makers like Apple have thwarted all requests. Late last year, India's Department of Communications gave smartphone companies 90 days to start preinstalling the Sanchar Saathi government app on all new devices sold in the country. Sanchar Saathi is a government app that lets users block stolen devices, report fraudulent calls, and verify second-hand phones. Apple told government officials that it would not comply with the requirement because of privacy and security concerns, and the government dropped the issue. Apple told India the same thing about the Aadhaar app, informing the IT ministry that it had safety and security concerns about preloading apps.Tag: IndiaThis article, "India Won't Require Apple to Preinstall Government ID App on iPhones" first appeared on MacRumors.comDiscuss this article in our forums

Article URL: https://www.corsix.org/content/simplified-model-of-fil-c Comments URL: https://news.ycombinator.com/item?id=47810872 Points: 179 # Comments: 98

Last month, OpenAI gave up on its Sora video generation tool, and on Friday, the Sora team's leader, Bill Peebles, announced that he is leaving the company. OpenAI has been shifting its priorities as part of an effort to avoid "side quests," and Peebles' departure is just one of many recent changes as the company moves to focus more on coding and enterprise use. As part of a note Peebles posted on X, he said: I am immensely grateful to Sam, Mark, Aditya and Jakub for fostering a research environment that allowed us to pursue ideas off-the-beaten path from the company's mainline roadmap. It's tempting in life to mode collapse to the most i … Read the full story at The Verge.

After rolling out to Google AI subscribers earlier this month, the Gemini app has now launched notebooks to free users. more…

Tinder users who prove they're a real person by visiting an identity-verifying orb will soon be able to get five free boosts in the app - and it's just the latest service to embrace the orb. World, which was co-founded by OpenAI CEO Sam Altman, initially tested Tinder verification using its facial scanning orbs through a pilot program in Japan last year. It's now expanding the service to "select markets, including Japan and the United States." To verify that they're not a bot or an AI agent, users have to physically visit one of World's orbs in person. According to World, the orb "takes pictures of your face and eyes, then encrypts and sto … Read the full story at The Verge.

Welcome to episode 96 of Pixelated, a podcast by 9to5Google. This week, Damien, Abner, and Will talk through Google’s new native Gemini app for Mac and wonder why now, and why we don’t see more standalone applications from the company. They also dive into new reports surrounding Google’s portion of the foldable market — and the risk Apple holds against it — before finishing up with YouTube’s new workaround for disabling Shorts. Subscribe YouTube Podcasts Pocket Casts Spotify Apple Podcasts Overcast Sponsored by Proton Unlimited: Pixelated listeners can save 30% on an annual subscription to the company’s suite of privacy-friendly services by signing up using our link. Thanks to Proton Unlimited for sponsoring the podcast. more…

The Trump administration has spent nearly two months fighting with AI company Anthropic. It's dubbed the company a "RADICAL LEFT, WOKE COMPANY" full of "Leftwing nut jobs" and a menace to national security. But some of the ice may reportedly be melting between the two, thanks to Anthropic's buzzy new cybersecurity-focused model: Claude Mythos Preview. Anthropic's relationship with the Pentagon soured quickly in late February after the company refused to budge on two red lines: using its technology for domestic mass surveillance or lethal fully autonomous weapons with no human in the loop. Anthropic's tech has in the past been used heavily b … Read the full story at The Verge.

Article URL: https://electrek.co/2026/04/17/tesla-hw3-owners-be-patient-7-years-fsd/ Comments URL: https://news.ycombinator.com/item?id=47809347 Points: 201 # Comments: 166

Amazon this week announced plans to acquire Globalstar, the satellite company that powers Apple's satellite features on the iPhone 14 and newer and the Apple Watch Ultra 3. In turn, Amazon announced that it has signed an agreement with Apple to provide satellite connectivity for current and future iPhone and Apple Watch features. The transaction, subject to regulatory approval, is expected to close in 2027. At that point, Apple's features will be powered by Amazon Leo satellites. Apple's current satellite features:Emergency SOS via satellite Find My via satellite Roadside Assistance via satellite Messages via satellite All of the features are currently free to use in supported areas without Wi-Fi or cellular connectivity. Availability varies by country. There were already five more iPhone satellite features or enhancements rumored to be in the works, even before Amazon announced this deal with Apple. At least some of the improvements may be part of iOS 27, which is expected to be available in beta starting in June and widely released in September this year. Those enhancements are as follows:5G via satellite (may be exclusive to iPhone 18 Pro and iPhone 18 Pro Max) Apple Maps via satellite Photos support for Messages via satellite Third-party apps in the App Store will be able to integrate Apple's satellite features The ability to connect an iPhone to a satellite without pointing the device toward the skyAmazon's announcement mentioned future features, too, so Apple's suite of satellite functions should expand even more over the coming years.Related Roundup: iOS 27Tag: iPhone Satellite FeaturesThis article, "iPhones to Get These New Satellite Features" first appeared on MacRumors.comDiscuss this article in our forums

Article URL: https://blog.calif.io/p/mad-bugs-even-cat-readmetxt-is-not Comments URL: https://news.ycombinator.com/item?id=47809190 Points: 202 # Comments: 116

Article URL: https://www.esa.int/Science_Exploration/Human_and_Robotic_Exploration/The_toxic_side_of_the_Moon Comments URL: https://news.ycombinator.com/item?id=47808913 Points: 349 # Comments: 202

Prediction market exchanges have created an environment where just about any piece of information is potentially monetizable: How well will BTS's new song perform this week? How hot will Los Angeles get? Will Donald Trump be impeached? Users can wager on all of that and, on some platforms, more gruesome and violent outcomes in the real world. The rapid rise and expansion of Polymarket and Kalshi have put newsrooms in a strange position. Prediction market evangelists often claim that their odds are more trustworthy and accurate than polls and traditional media - effectively positioning the industry as a replacement for news. At the same time … Read the full story at The Verge.

Samsung is still working on One UI 9 ahead of a planned launch later this summer. With a fresh leaked build, we’re getting a better glimpse at two features coming to your phone with this update. more…

Your Friday afternoon lineup of the best Android game and app deals is now ready to roll, including titles like Super Onion Boy 2, Kingdomino, Dungeon Tracer, 911 Operator, ALTER EGO COMPLEX, BE-A Walker, and more. Just be sure to dive into the deals have on Galaxy S26 Ultra and new Galaxy Buds 4 Pro at $325 off alongside a chance to score Google’s most affordable unlocked Pixel 10 at up to $354 off, but all of the apps await below. more…

I kind of wish it just took pictures. I've never been as charmed and frustrated by one gadget as I have with the Poetry Camera. It's a delightful object. White and cherry red with a color-matched woven strap, it looks playful and adorably lo-fi. If I saw it on a store shelf, I'd absolutely pick it up. But aside from obviously appealing, I'm not exactly sure what it is. I mean, I know what it is. It's a camera that makes AI poems instead of photos. You take a picture, and instead of printing a photo, you get an AI-generated poem inspired by the scene, printed on thermal receipt paper. But after printing dozens of poems, I can only report feeling frustrated instead of inspired. … Read the full story at The Verge.

Following one last restock earlier this month, Samsung now says that the “limited-run” Galaxy Z TriFold is “completely sold out” both online and in stores. more…